diff --git a/doc/source/whatsnew/v1.4.0.rst b/doc/source/whatsnew/v1.4.0.rst
index 450ecc85c725b..d2683ebf4694a 100644
--- a/doc/source/whatsnew/v1.4.0.rst
+++ b/doc/source/whatsnew/v1.4.0.rst
@@ -276,7 +276,7 @@ Timedelta
 
 Timezones
 ^^^^^^^^^
--
+- Bug in :meth:`Series.dt.tz_convert` resetting index in a :class:`Series` with :class:`CategoricalIndex` (:issue:`43080`)
 -
 
 Numeric
@@ -315,6 +315,7 @@ Indexing
 - Bug in :meth:`DataFrame.drop` where the error message did not show missing labels with commas when raising ``KeyError`` (:issue:`42881`)
 -
 
+
 Missing
 ^^^^^^^
 - Bug in :meth:`DataFrame.fillna` with limit and no method ignores axis='columns' or ``axis = 1`` (:issue:`40989`)
diff --git a/pandas/core/indexes/accessors.py b/pandas/core/indexes/accessors.py
index 516c63e0e3727..b8f4b5f9d3423 100644
--- a/pandas/core/indexes/accessors.py
+++ b/pandas/core/indexes/accessors.py
@@ -492,6 +492,7 @@ def __new__(cls, data: Series):
                 name=orig.name,
                 copy=False,
                 dtype=orig._values.categories.dtype,
+                index=orig.index,
             )
 
         if is_datetime64_dtype(data.dtype):
diff --git a/pandas/tests/series/accessors/test_dt_accessor.py b/pandas/tests/series/accessors/test_dt_accessor.py
index 61a22dad5d09b..eb7e1d4268605 100644
--- a/pandas/tests/series/accessors/test_dt_accessor.py
+++ b/pandas/tests/series/accessors/test_dt_accessor.py
@@ -691,6 +691,19 @@ def test_isocalendar(self, input_series, expected_output):
         )
         tm.assert_frame_equal(result, expected_frame)
 
+    def test_hour_index(self):
+        dt_series = Series(
+            date_range(start="2021-01-01", periods=5, freq="h"),
+            index=[2, 6, 7, 8, 11],
+            dtype="category",
+        )
+        result = dt_series.dt.hour
+        expected = Series(
+            [0, 1, 2, 3, 4],
+            index=[2, 6, 7, 8, 11],
+        )
+        tm.assert_series_equal(result, expected)
+
 
 class TestSeriesPeriodValuesDtAccessor:
     @pytest.mark.parametrize(
diff --git a/pandas/tests/series/methods/test_tz_localize.py b/pandas/tests/series/methods/test_tz_localize.py
index 4d7f26076e060..a32c1fb8df502 100644
--- a/pandas/tests/series/methods/test_tz_localize.py
+++ b/pandas/tests/series/methods/test_tz_localize.py
@@ -41,6 +41,23 @@ def test_series_tz_localize_ambiguous_bool(self):
         result = ser.dt.tz_localize("US/Central", ambiguous=[False])
         tm.assert_series_equal(result, expected1)
 
+    def test_series_tz_localize_matching_index(self):
+        # Matching the index of the result with that of the original series
+        # GH 43080
+        dt_series = Series(
+            date_range(start="2021-01-01T02:00:00", periods=5, freq="1D"),
+            index=[2, 6, 7, 8, 11],
+            dtype="category",
+        )
+        result = dt_series.dt.tz_localize("Europe/Berlin")
+        expected = Series(
+            date_range(
+                start="2021-01-01T02:00:00", periods=5, freq="1D", tz="Europe/Berlin"
+            ),
+            index=[2, 6, 7, 8, 11],
+        )
+        tm.assert_series_equal(result, expected)
+
     @pytest.mark.parametrize("tz", ["Europe/Warsaw", "dateutil/Europe/Warsaw"])
     @pytest.mark.parametrize(
         "method, exp",