diff --git a/doc/source/whatsnew/v1.0.2.rst b/doc/source/whatsnew/v1.0.2.rst
index 462f243f14494..7a25f7b58c2e7 100644
--- a/doc/source/whatsnew/v1.0.2.rst
+++ b/doc/source/whatsnew/v1.0.2.rst
@@ -64,6 +64,7 @@ Bug fixes
 **Datetimelike**
 
 - Bug in :meth:`DataFrame.reindex` and :meth:`Series.reindex` when reindexing with a tz-aware index (:issue:`26683`)
+- Bug in :meth:`Series.astype` not copying for tz-naive and tz-aware datetime64 dtype (:issue:`32490`)
 - Bug where :func:`to_datetime` would raise when passed ``pd.NA`` (:issue:`32213`)
 
 **Categorical**
@@ -84,6 +85,7 @@ Bug fixes
 - Fixed bug in setting values using a slice indexer with string dtype (:issue:`31772`)
 - Fixed bug where :meth:`GroupBy.first` and :meth:`GroupBy.last` would raise a ``TypeError`` when groups contained ``pd.NA`` in a column of object dtype (:issue:`32123`)
 - Fix bug in :meth:`Series.convert_dtypes` for series with mix of integers and strings (:issue:`32117`)
+- Fixed bug in :meth:`DataFrame.convert_dtypes`, where ``BooleanDtype`` columns were converted to ``Int64`` (:issue:`32287`)
 
 **Strings**
 
diff --git a/pandas/core/arrays/datetimes.py b/pandas/core/arrays/datetimes.py
index 9f19c7ba0be6e..7223eda22b3d9 100644
--- a/pandas/core/arrays/datetimes.py
+++ b/pandas/core/arrays/datetimes.py
@@ -587,6 +587,8 @@ def astype(self, dtype, copy=True):
             if getattr(self.dtype, "tz", None) is None:
                 return self.tz_localize(new_tz)
             result = self.tz_convert(new_tz)
+            if copy:
+                result = result.copy()
             if new_tz is None:
                 # Do we want .astype('datetime64[ns]') to be an ndarray.
                 # The astype in Block._astype expects this to return an
diff --git a/pandas/core/dtypes/cast.py b/pandas/core/dtypes/cast.py
index 7dac36b53fce5..97c02428cbdf9 100644
--- a/pandas/core/dtypes/cast.py
+++ b/pandas/core/dtypes/cast.py
@@ -1049,7 +1049,8 @@ def convert_dtypes(
     dtype
         new dtype
     """
-    if convert_string or convert_integer or convert_boolean:
+    is_extension = is_extension_array_dtype(input_array.dtype)
+    if (convert_string or convert_integer or convert_boolean) and not is_extension:
         try:
             inferred_dtype = lib.infer_dtype(input_array)
         except ValueError:
@@ -1062,9 +1063,7 @@ def convert_dtypes(
         if convert_integer:
             target_int_dtype = "Int64"
 
-            if is_integer_dtype(input_array.dtype) and not is_extension_array_dtype(
-                input_array.dtype
-            ):
+            if is_integer_dtype(input_array.dtype):
                 from pandas.core.arrays.integer import _dtypes
 
                 inferred_dtype = _dtypes.get(input_array.dtype.name, target_int_dtype)
@@ -1078,9 +1077,7 @@ def convert_dtypes(
                 inferred_dtype = input_array.dtype
 
         if convert_boolean:
-            if is_bool_dtype(input_array.dtype) and not is_extension_array_dtype(
-                input_array.dtype
-            ):
+            if is_bool_dtype(input_array.dtype):
                 inferred_dtype = "boolean"
         else:
             if isinstance(inferred_dtype, str) and inferred_dtype == "boolean":
diff --git a/pandas/core/internals/blocks.py b/pandas/core/internals/blocks.py
index c088b7020927b..bce440fe09319 100644
--- a/pandas/core/internals/blocks.py
+++ b/pandas/core/internals/blocks.py
@@ -2228,6 +2228,9 @@ def astype(self, dtype, copy: bool = False, errors: str = "raise"):
         # if we are passed a datetime64[ns, tz]
         if is_datetime64tz_dtype(dtype):
             values = self.values
+            if copy:
+                # this should be the only copy
+                values = values.copy()
             if getattr(values, "tz", None) is None:
                 values = DatetimeArray(values).tz_localize("UTC")
             values = values.tz_convert(dtype.tz)
diff --git a/pandas/tests/arrays/test_datetimes.py b/pandas/tests/arrays/test_datetimes.py
index a59ed429cc404..2c26e72a245f7 100644
--- a/pandas/tests/arrays/test_datetimes.py
+++ b/pandas/tests/arrays/test_datetimes.py
@@ -151,6 +151,18 @@ def test_astype_to_same(self):
         result = arr.astype(DatetimeTZDtype(tz="US/Central"), copy=False)
         assert result is arr
 
+    @pytest.mark.parametrize("dtype", ["datetime64[ns]", "datetime64[ns, UTC]"])
+    @pytest.mark.parametrize(
+        "other", ["datetime64[ns]", "datetime64[ns, UTC]", "datetime64[ns, CET]"]
+    )
+    def test_astype_copies(self, dtype, other):
+        # https://github.com/pandas-dev/pandas/pull/32490
+        s = pd.Series([1, 2], dtype=dtype)
+        orig = s.copy()
+        t = s.astype(other)
+        t[:] = pd.NaT
+        tm.assert_series_equal(s, orig)
+
     @pytest.mark.parametrize("dtype", [int, np.int32, np.int64, "uint32", "uint64"])
     def test_astype_int(self, dtype):
         arr = DatetimeArray._from_sequence([pd.Timestamp("2000"), pd.Timestamp("2001")])
diff --git a/pandas/tests/series/methods/test_convert_dtypes.py b/pandas/tests/series/methods/test_convert_dtypes.py
index 17527a09f07a1..a41f893e3753f 100644
--- a/pandas/tests/series/methods/test_convert_dtypes.py
+++ b/pandas/tests/series/methods/test_convert_dtypes.py
@@ -279,3 +279,8 @@ def test_convert_string_dtype(self):
         )
         result = df.convert_dtypes()
         tm.assert_frame_equal(df, result)
+
+    def test_convert_bool_dtype(self):
+        # GH32287
+        df = pd.DataFrame({"A": pd.array([True])})
+        tm.assert_frame_equal(df, df.convert_dtypes())