diff --git a/pandas/core/indexes/category.py b/pandas/core/indexes/category.py
index ecf77a9987bee..059c36a901297 100644
--- a/pandas/core/indexes/category.py
+++ b/pandas/core/indexes/category.py
@@ -354,11 +354,6 @@ def __contains__(self, key: Any) -> bool:
 
         return contains(self, key, container=self._engine)
 
-    @doc(Index.astype)
-    def astype(self, dtype, copy=True):
-        res_data = self._data.astype(dtype, copy=copy)
-        return Index(res_data, name=self.name)
-
     @doc(Index.fillna)
     def fillna(self, value, downcast=None):
         value = self._require_scalar(value)
diff --git a/pandas/core/indexes/extension.py b/pandas/core/indexes/extension.py
index 73f96b2f6ad41..661adde44089c 100644
--- a/pandas/core/indexes/extension.py
+++ b/pandas/core/indexes/extension.py
@@ -11,7 +11,7 @@
 from pandas.errors import AbstractMethodError
 from pandas.util._decorators import cache_readonly, doc
 
-from pandas.core.dtypes.common import is_dtype_equal, is_object_dtype
+from pandas.core.dtypes.common import is_dtype_equal, is_object_dtype, pandas_dtype
 from pandas.core.dtypes.generic import ABCDataFrame, ABCSeries
 
 from pandas.core.arrays import ExtensionArray
@@ -294,9 +294,12 @@ def map(self, mapper, na_action=None):
 
     @doc(Index.astype)
     def astype(self, dtype, copy=True):
-        if is_dtype_equal(self.dtype, dtype) and copy is False:
-            # Ensure that self.astype(self.dtype) is self
-            return self
+        dtype = pandas_dtype(dtype)
+        if is_dtype_equal(self.dtype, dtype):
+            if not copy:
+                # Ensure that self.astype(self.dtype) is self
+                return self
+            return self.copy()
 
         new_values = self._data.astype(dtype, copy=copy)
 
diff --git a/pandas/core/internals/blocks.py b/pandas/core/internals/blocks.py
index 0bd60931f9a7e..6500cfcd9ea5a 100644
--- a/pandas/core/internals/blocks.py
+++ b/pandas/core/internals/blocks.py
@@ -649,15 +649,7 @@ def astype(self, dtype, copy: bool = False, errors: str = "raise"):
     def _astype(self, dtype: DtypeObj, copy: bool) -> ArrayLike:
         values = self.values
 
-        if is_categorical_dtype(dtype):
-
-            if is_categorical_dtype(values.dtype):
-                # GH#10696/GH#18593: update an existing categorical efficiently
-                return values.astype(dtype, copy=copy)
-
-            return Categorical(values, dtype=dtype)
-
-        elif is_datetime64tz_dtype(dtype) and is_datetime64_dtype(values.dtype):
+        if is_datetime64tz_dtype(dtype) and is_datetime64_dtype(values.dtype):
             # if we are passed a datetime64[ns, tz]
             if copy:
                 # this should be the only copy