diff --git a/pandas/core/arrays/datetimes.py b/pandas/core/arrays/datetimes.py
index e42402b307f28..b19bd2240ca9e 100644
--- a/pandas/core/arrays/datetimes.py
+++ b/pandas/core/arrays/datetimes.py
@@ -589,6 +589,8 @@ 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 4d99a13ccd0b5..eecb1e567bd8f 100644
--- a/pandas/core/dtypes/cast.py
+++ b/pandas/core/dtypes/cast.py
@@ -1045,8 +1045,8 @@ 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:
@@ -1059,9 +1059,7 @@ 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)
@@ -1075,9 +1073,7 @@ 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 db98ec5ad388e..33a5d6443aa7c 100644
--- a/pandas/core/internals/blocks.py
+++ b/pandas/core/internals/blocks.py
@@ -2209,6 +2209,9 @@ 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 5608ab5fbd9db..925781b6c4851 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/test_convert_dtypes.py b/pandas/tests/series/test_convert_dtypes.py
index 17527a09f07a1..a41f893e3753f 100644
--- a/pandas/tests/series/test_convert_dtypes.py
+++ b/pandas/tests/series/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())