diff --git a/doc/source/whatsnew/v1.0.4.rst b/doc/source/whatsnew/v1.0.4.rst
index d4f4e9c0ae8de..4f122b0dea5f4 100644
--- a/doc/source/whatsnew/v1.0.4.rst
+++ b/doc/source/whatsnew/v1.0.4.rst
@@ -21,6 +21,7 @@ Fixed regressions
 - Fix performance regression in ``memory_usage(deep=True)`` for object dtype (:issue:`33012`)
 - Bug where :meth:`Categorical.replace` would replace with ``NaN`` whenever the new value and replacement value were equal (:issue:`33288`)
 - Bug where an ordered :class:`Categorical` containing only ``NaN`` values would raise rather than returning ``NaN`` when taking the minimum or maximum  (:issue:`33450`)
+- Bug in :meth:`DataFrameGroupBy.agg` with dictionary input losing ``ExtensionArray`` dtypes (:issue:`32194`)
 - Fix to preserve the ability to index with the "nearest" method with xarray's CFTimeIndex, an :class:`Index` subclass (`pydata/xarray#3751 <https://github.com/pydata/xarray/issues/3751>`_, :issue:`32905`).
 - 
 
@@ -28,6 +29,7 @@ Fixed regressions
 
 Bug fixes
 ~~~~~~~~~
+- Bug in :meth:`SeriesGroupBy.first`, :meth:`SeriesGroupBy.last`, :meth:`SeriesGroupBy.min`, and :meth:`SeriesGroupBy.max` returning floats when applied to nullable Booleans (:issue:`33071`)
 - Bug in :meth:`Rolling.min` and :meth:`Rolling.max`: Growing memory usage after multiple calls when using a fixed window (:issue:`30726`)
 - 
 
diff --git a/pandas/core/groupby/groupby.py b/pandas/core/groupby/groupby.py
index 57d865a051c31..478239b1bcff0 100644
--- a/pandas/core/groupby/groupby.py
+++ b/pandas/core/groupby/groupby.py
@@ -42,6 +42,7 @@ class providing the base-class of operations.
 from pandas.core.dtypes.cast import maybe_downcast_to_dtype
 from pandas.core.dtypes.common import (
     ensure_float,
+    is_categorical_dtype,
     is_datetime64_dtype,
     is_extension_array_dtype,
     is_integer_dtype,
@@ -807,15 +808,15 @@ def _try_cast(self, result, obj, numeric_only: bool = False):
             dtype = obj.dtype
 
         if not is_scalar(result):
-            if is_extension_array_dtype(dtype) and dtype.kind != "M":
-                # The function can return something of any type, so check
-                #  if the type is compatible with the calling EA.
-                # datetime64tz is handled correctly in agg_series,
-                #  so is excluded here.
-
-                if len(result) and isinstance(result[0], dtype.type):
-                    cls = dtype.construct_array_type()
-                    result = try_cast_to_ea(cls, result, dtype=dtype)
+            if (
+                is_extension_array_dtype(dtype)
+                and not is_categorical_dtype(dtype)
+                and dtype.kind != "M"
+            ):
+                # We have to special case categorical so as not to upcast
+                # things like counts back to categorical
+                cls = dtype.construct_array_type()
+                result = try_cast_to_ea(cls, result, dtype=dtype)
 
             elif numeric_only and is_numeric_dtype(dtype) or not numeric_only:
                 result = maybe_downcast_to_dtype(result, dtype)
diff --git a/pandas/tests/groupby/test_nth.py b/pandas/tests/groupby/test_nth.py
index 7b2e3f7a7e06a..947907caf5cbc 100644
--- a/pandas/tests/groupby/test_nth.py
+++ b/pandas/tests/groupby/test_nth.py
@@ -395,6 +395,32 @@ def test_first_last_tz_multi_column(method, ts, alpha):
     tm.assert_frame_equal(result, expected)
 
 
+@pytest.mark.parametrize(
+    "values",
+    [
+        pd.array([True, False], dtype="boolean"),
+        pd.array([1, 2], dtype="Int64"),
+        pd.to_datetime(["2020-01-01", "2020-02-01"]),
+        pd.to_timedelta([1, 2], unit="D"),
+    ],
+)
+@pytest.mark.parametrize("function", ["first", "last", "min", "max"])
+def test_first_last_extension_array_keeps_dtype(values, function):
+    # https://github.com/pandas-dev/pandas/issues/33071
+    # https://github.com/pandas-dev/pandas/issues/32194
+    df = DataFrame({"a": [1, 2], "b": values})
+    grouped = df.groupby("a")
+    idx = Index([1, 2], name="a")
+    expected_series = Series(values, name="b", index=idx)
+    expected_frame = DataFrame({"b": values}, index=idx)
+
+    result_series = getattr(grouped["b"], function)()
+    tm.assert_series_equal(result_series, expected_series)
+
+    result_frame = grouped.agg({"b": function})
+    tm.assert_frame_equal(result_frame, expected_frame)
+
+
 def test_nth_multi_index_as_expected():
     # PR 9090, related to issue 8979
     # test nth on MultiIndex
diff --git a/pandas/tests/resample/test_datetime_index.py b/pandas/tests/resample/test_datetime_index.py
index 3ad82b9e075a8..ab6985b11ba9a 100644
--- a/pandas/tests/resample/test_datetime_index.py
+++ b/pandas/tests/resample/test_datetime_index.py
@@ -122,9 +122,7 @@ def test_resample_integerarray():
 
     result = ts.resample("3T").mean()
     expected = Series(
-        [1, 4, 7],
-        index=pd.date_range("1/1/2000", periods=3, freq="3T"),
-        dtype="float64",
+        [1, 4, 7], index=pd.date_range("1/1/2000", periods=3, freq="3T"), dtype="Int64",
     )
     tm.assert_series_equal(result, expected)