diff --git a/pandas/_libs/algos_common_helper.pxi.in b/pandas/_libs/algos_common_helper.pxi.in
index 1efef480f3a29..ed4c0e4c59609 100644
--- a/pandas/_libs/algos_common_helper.pxi.in
+++ b/pandas/_libs/algos_common_helper.pxi.in
@@ -45,7 +45,7 @@ def get_dispatch(dtypes):
 
 @cython.wraparound(False)
 @cython.boundscheck(False)
-cpdef map_indices_{{name}}(ndarray[{{c_type}}] index):
+def map_indices_{{name}}(ndarray[{{c_type}}] index):
     """
     Produce a dict mapping the values of the input array to their respective
     locations.
@@ -542,7 +542,7 @@ def put2d_{{name}}_{{dest_type}}(ndarray[{{c_type}}, ndim=2, cast=True] values,
 cdef int PLATFORM_INT = (<ndarray> np.arange(0, dtype=np.intp)).descr.type_num
 
 
-cpdef ensure_platform_int(object arr):
+def ensure_platform_int(object arr):
     # GH3033, GH1392
     # platform int is the size of the int pointer, e.g. np.intp
     if util.is_array(arr):
@@ -554,7 +554,7 @@ cpdef ensure_platform_int(object arr):
         return np.array(arr, dtype=np.intp)
 
 
-cpdef ensure_object(object arr):
+def ensure_object(object arr):
     if util.is_array(arr):
         if (<ndarray> arr).descr.type_num == NPY_OBJECT:
             return arr
@@ -587,7 +587,7 @@ def get_dispatch(dtypes):
 
 {{for name, c_type, dtype in get_dispatch(dtypes)}}
 
-cpdef ensure_{{name}}(object arr, copy=True):
+def ensure_{{name}}(object arr, copy=True):
     if util.is_array(arr):
         if (<ndarray> arr).descr.type_num == NPY_{{c_type}}:
             return arr
diff --git a/pandas/_libs/groupby.pyx b/pandas/_libs/groupby.pyx
index d8feda9ef27ef..d683c93c9b32e 100644
--- a/pandas/_libs/groupby.pyx
+++ b/pandas/_libs/groupby.pyx
@@ -67,6 +67,7 @@ cdef inline float64_t median_linear(float64_t* a, int n) nogil:
     return result
 
 
+# TODO: Is this redundant with algos.kth_smallest?
 cdef inline float64_t kth_smallest_c(float64_t* a,
                                      Py_ssize_t k,
                                      Py_ssize_t n) nogil:
diff --git a/pandas/_libs/hashing.pyx b/pandas/_libs/hashing.pyx
index 557e3e34aee25..88b4d97de492c 100644
--- a/pandas/_libs/hashing.pyx
+++ b/pandas/_libs/hashing.pyx
@@ -132,6 +132,7 @@ cdef inline void _sipround(uint64_t* v0, uint64_t* v1,
     v2[0] = _rotl(v2[0], 32)
 
 
+# TODO: This appears unused; remove?
 cpdef uint64_t siphash(bytes data, bytes key) except? 0:
     if len(key) != 16:
         raise ValueError("key should be a 16-byte bytestring, "
diff --git a/pandas/_libs/index.pyx b/pandas/_libs/index.pyx
index 9c906a00bd4fe..d5846f2b42378 100644
--- a/pandas/_libs/index.pyx
+++ b/pandas/_libs/index.pyx
@@ -49,7 +49,7 @@ cpdef get_value_at(ndarray arr, object loc, object tz=None):
     return util.get_value_at(arr, loc)
 
 
-cpdef object get_value_box(ndarray arr, object loc):
+def get_value_box(arr: ndarray, loc: object) -> object:
     return get_value_at(arr, loc, tz=None)
 
 
diff --git a/pandas/_libs/internals.pyx b/pandas/_libs/internals.pyx
index 97cc7f96cb24f..996570dae3302 100644
--- a/pandas/_libs/internals.pyx
+++ b/pandas/_libs/internals.pyx
@@ -184,7 +184,7 @@ cdef class BlockPlacement:
         return self._as_slice
 
 
-cpdef slice_canonize(slice s):
+cdef slice_canonize(slice s):
     """
     Convert slice to canonical bounded form.
     """
@@ -255,7 +255,7 @@ cpdef Py_ssize_t slice_len(
     return length
 
 
-cpdef slice_get_indices_ex(slice slc, Py_ssize_t objlen=PY_SSIZE_T_MAX):
+cdef slice_get_indices_ex(slice slc, Py_ssize_t objlen=PY_SSIZE_T_MAX):
     """
     Get (start, stop, step, length) tuple for a slice.
 
diff --git a/pandas/_libs/interval.pyx b/pandas/_libs/interval.pyx
index 5ae20a27c2381..d8e2e8eb4b4ea 100644
--- a/pandas/_libs/interval.pyx
+++ b/pandas/_libs/interval.pyx
@@ -362,8 +362,8 @@ cdef class Interval(IntervalMixin):
 
 @cython.wraparound(False)
 @cython.boundscheck(False)
-cpdef intervals_to_interval_bounds(ndarray intervals,
-                                   bint validate_closed=True):
+def intervals_to_interval_bounds(ndarray intervals,
+                                 bint validate_closed=True):
     """
     Parameters
     ----------
@@ -415,4 +415,5 @@ cpdef intervals_to_interval_bounds(ndarray intervals,
 
     return left, right, closed
 
+
 include "intervaltree.pxi"
diff --git a/pandas/_libs/lib.pyx b/pandas/_libs/lib.pyx
index a6078da28a3ba..6b425d7022ecd 100644
--- a/pandas/_libs/lib.pyx
+++ b/pandas/_libs/lib.pyx
@@ -107,7 +107,7 @@ def memory_usage_of_objects(object[:] arr):
 # ----------------------------------------------------------------------
 
 
-cpdef bint is_scalar(object val):
+def is_scalar(val: object) -> bint:
     """
     Return True if given value is scalar.
 
@@ -137,7 +137,7 @@ cpdef bint is_scalar(object val):
             or util.is_period_object(val)
             or is_decimal(val)
             or is_interval(val)
-            or is_offset(val))
+            or util.is_offset_object(val))
 
 
 def item_from_zerodim(object val):
@@ -457,7 +457,7 @@ def maybe_booleans_to_slice(ndarray[uint8_t] mask):
 
 @cython.wraparound(False)
 @cython.boundscheck(False)
-cpdef bint array_equivalent_object(object[:] left, object[:] right):
+def array_equivalent_object(left: object[:], right: object[:]) -> bint:
     """ perform an element by element comparion on 1-d object arrays
         taking into account nan positions """
     cdef:
@@ -497,7 +497,7 @@ def astype_intsafe(ndarray[object] arr, new_dtype):
     return result
 
 
-cpdef ndarray[object] astype_unicode(ndarray arr):
+def astype_unicode(arr: ndarray) -> ndarray[object]:
     cdef:
         Py_ssize_t i, n = arr.size
         ndarray[object] result = np.empty(n, dtype=object)
@@ -508,7 +508,7 @@ cpdef ndarray[object] astype_unicode(ndarray arr):
     return result
 
 
-cpdef ndarray[object] astype_str(ndarray arr):
+def astype_str(arr: ndarray) -> ndarray[object]:
     cdef:
         Py_ssize_t i, n = arr.size
         ndarray[object] result = np.empty(n, dtype=object)
@@ -791,19 +791,19 @@ def indices_fast(object index, ndarray[int64_t] labels, list keys,
 
 # core.common import for fast inference checks
 
-cpdef bint is_float(object obj):
+def is_float(obj: object) -> bint:
     return util.is_float_object(obj)
 
 
-cpdef bint is_integer(object obj):
+def is_integer(obj: object) -> bint:
     return util.is_integer_object(obj)
 
 
-cpdef bint is_bool(object obj):
+def is_bool(obj: object) -> bint:
     return util.is_bool_object(obj)
 
 
-cpdef bint is_complex(object obj):
+def is_complex(obj: object) -> bint:
     return util.is_complex_object(obj)
 
 
@@ -815,15 +815,11 @@ cpdef bint is_interval(object obj):
     return getattr(obj, '_typ', '_typ') == 'interval'
 
 
-cpdef bint is_period(object val):
+def is_period(val: object) -> bint:
     """ Return a boolean if this is a Period object """
     return util.is_period_object(val)
 
 
-cdef inline bint is_offset(object val):
-    return getattr(val, '_typ', '_typ') == 'dateoffset'
-
-
 _TYPE_MAP = {
     'categorical': 'categorical',
     'category': 'categorical',
@@ -1225,7 +1221,7 @@ def infer_dtype(object value, bint skipna=False):
         if is_bytes_array(values, skipna=skipna):
             return 'bytes'
 
-    elif is_period(val):
+    elif util.is_period_object(val):
         if is_period_array(values):
             return 'period'
 
@@ -1243,7 +1239,7 @@ def infer_dtype(object value, bint skipna=False):
     return 'mixed'
 
 
-cpdef object infer_datetimelike_array(object arr):
+def infer_datetimelike_array(arr: object) -> object:
     """
     infer if we have a datetime or timedelta array
     - date: we have *only* date and maybe strings, nulls
@@ -1580,7 +1576,7 @@ cpdef bint is_datetime64_array(ndarray values):
     return validator.validate(values)
 
 
-cpdef bint is_datetime_with_singletz_array(ndarray values):
+def is_datetime_with_singletz_array(values: ndarray) -> bint:
     """
     Check values have the same tzinfo attribute.
     Doesn't check values are datetime-like types.
@@ -1616,7 +1612,8 @@ cdef class TimedeltaValidator(TemporalValidator):
         return is_null_timedelta64(value)
 
 
-cpdef bint is_timedelta_array(ndarray values):
+# TODO: Not used outside of tests; remove?
+def is_timedelta_array(values: ndarray) -> bint:
     cdef:
         TimedeltaValidator validator = TimedeltaValidator(len(values),
                                                           skipna=True)
@@ -1628,7 +1625,8 @@ cdef class Timedelta64Validator(TimedeltaValidator):
         return util.is_timedelta64_object(value)
 
 
-cpdef bint is_timedelta64_array(ndarray values):
+# TODO: Not used outside of tests; remove?
+def is_timedelta64_array(values: ndarray) -> bint:
     cdef:
         Timedelta64Validator validator = Timedelta64Validator(len(values),
                                                               skipna=True)
@@ -1672,7 +1670,7 @@ cpdef bint is_time_array(ndarray values, bint skipna=False):
 
 cdef class PeriodValidator(TemporalValidator):
     cdef inline bint is_value_typed(self, object value) except -1:
-        return is_period(value)
+        return util.is_period_object(value)
 
     cdef inline bint is_valid_null(self, object value) except -1:
         return is_null_period(value)
diff --git a/pandas/_libs/tslib.pyx b/pandas/_libs/tslib.pyx
index bdd279b19208b..93fae695d51fd 100644
--- a/pandas/_libs/tslib.pyx
+++ b/pandas/_libs/tslib.pyx
@@ -300,7 +300,7 @@ def format_array_from_datetime(ndarray[int64_t] values, object tz=None,
     return result
 
 
-cpdef array_with_unit_to_datetime(ndarray values, unit, errors='coerce'):
+def array_with_unit_to_datetime(ndarray values, unit, errors='coerce'):
     """
     convert the ndarray according to the unit
     if errors:
diff --git a/pandas/_libs/writers.pyx b/pandas/_libs/writers.pyx
index 796f4b754857e..8e55ffad8d231 100644
--- a/pandas/_libs/writers.pyx
+++ b/pandas/_libs/writers.pyx
@@ -3,8 +3,7 @@
 cimport cython
 from cython cimport Py_ssize_t
 
-from cpython cimport (PyString_Check, PyBytes_Check, PyUnicode_Check,
-                      PyBytes_GET_SIZE, PyUnicode_GET_SIZE)
+from cpython cimport PyBytes_GET_SIZE, PyUnicode_GET_SIZE
 
 try:
     from cpython cimport PyString_GET_SIZE
@@ -124,7 +123,7 @@ def convert_json_to_lines(object arr):
 # stata, pytables
 @cython.boundscheck(False)
 @cython.wraparound(False)
-cpdef Py_ssize_t max_len_string_array(pandas_string[:] arr):
+def max_len_string_array(pandas_string[:] arr) -> Py_ssize_t:
     """ return the maximum size of elements in a 1-dim string array """
     cdef:
         Py_ssize_t i, m = 0, l = 0, length = arr.shape[0]
@@ -132,11 +131,11 @@ cpdef Py_ssize_t max_len_string_array(pandas_string[:] arr):
 
     for i in range(length):
         v = arr[i]
-        if PyString_Check(v):
+        if isinstance(v, str):
             l = PyString_GET_SIZE(v)
-        elif PyBytes_Check(v):
+        elif isinstance(v, bytes):
             l = PyBytes_GET_SIZE(v)
-        elif PyUnicode_Check(v):
+        elif isinstance(v, unicode):
             l = PyUnicode_GET_SIZE(v)
 
         if l > m: