diff --git a/asv_bench/benchmarks/io/excel.py b/asv_bench/benchmarks/io/excel.py
index 80af2cff41769..e9776ff2c641e 100644
--- a/asv_bench/benchmarks/io/excel.py
+++ b/asv_bench/benchmarks/io/excel.py
@@ -11,7 +11,7 @@
 
 
 def _generate_dataframe():
-    N = 2000
+    N = 20000
     C = 5
     df = DataFrame(
         np.random.randn(N, C),
@@ -69,5 +69,9 @@ def time_read_excel(self, engine):
         fname = self.fname_odf if engine == "odf" else self.fname_excel
         read_excel(fname, engine=engine)
 
+    def nrows_read_excel(self, engine):
+        fname = self.fname_odf if engine == "odf" else self.fname_excel
+        read_excel(fname, engine=engine, nrows=1)
+
 
 from ..pandas_vb_common import setup  # noqa: F401 isort:skip
diff --git a/pandas/io/parsers.py b/pandas/io/parsers.py
index ede4fdc5e1d8b..ef3aad6080af9 100644
--- a/pandas/io/parsers.py
+++ b/pandas/io/parsers.py
@@ -1695,7 +1695,9 @@ def _convert_to_ndarrays(
         result = {}
         for c, values in dct.items():
             conv_f = None if converters is None else converters.get(c, None)
-            if isinstance(dtypes, dict):
+            if values.dtype != object:
+                cast_type = values.dtype
+            elif isinstance(dtypes, dict):
                 cast_type = dtypes.get(c, None)
             else:
                 # single dtype or None
@@ -3249,6 +3251,9 @@ def _make_date_converter(
 ):
     def converter(*date_cols):
         if date_parser is None:
+            date_cols = tuple(
+                x if isinstance(x, np.ndarray) else x.to_numpy() for x in date_cols
+            )
             strs = parsing.concat_date_cols(date_cols)
 
             try:
diff --git a/pandas/tests/io/parser/test_common.py b/pandas/tests/io/parser/test_common.py
index a6a9e5c5610f2..e48f205527677 100644
--- a/pandas/tests/io/parser/test_common.py
+++ b/pandas/tests/io/parser/test_common.py
@@ -18,7 +18,16 @@
 from pandas.errors import DtypeWarning, EmptyDataError, ParserError
 import pandas.util._test_decorators as td
 
-from pandas import DataFrame, Index, MultiIndex, Series, compat, concat, option_context
+from pandas import (
+    DataFrame,
+    Index,
+    MultiIndex,
+    Series,
+    compat,
+    concat,
+    option_context,
+    to_datetime,
+)
 import pandas._testing as tm
 
 from pandas.io.parsers import CParserWrapper, TextFileReader, TextParser
@@ -2182,6 +2191,20 @@ def test_no_header_two_extra_columns(all_parsers):
     tm.assert_frame_equal(df, ref)
 
 
+def test_dtype_with_parse_dates(all_parsers):
+    # GH 34066
+    parser = all_parsers
+    data = """
+a,b
+1,2020-05-23 01:00:00"""
+    expected = DataFrame(
+        [["1", "2020-05-23 01:00:00"]], columns=["a", "b"], dtype="string"
+    )
+    expected["b"] = to_datetime(expected["b"])
+    result = parser.read_csv(StringIO(data), dtype="string", parse_dates=["b"])
+    tm.assert_frame_equal(result, expected)
+
+
 def test_read_csv_names_not_accepting_sets(all_parsers):
     # GH 34946
     data = """\