diff --git a/doc/source/whatsnew/v1.1.4.rst b/doc/source/whatsnew/v1.1.4.rst
index 043b817bb9026..c5f7905bc8a20 100644
--- a/doc/source/whatsnew/v1.1.4.rst
+++ b/doc/source/whatsnew/v1.1.4.rst
@@ -21,6 +21,7 @@ Fixed regressions
 - Fixed regression in :meth:`Series.astype` converting ``None`` to ``"nan"`` when casting to string (:issue:`36904`)
 - Fixed regression in :class:`RollingGroupby` causing a segmentation fault with Index of dtype object (:issue:`36727`)
 - Fixed regression in :meth:`DataFrame.resample(...).apply(...)` raised ``AttributeError`` when input was a :class:`DataFrame` and only a :class:`Series` was evaluated (:issue:`36951`)
+- Fixed regression in ``DataFrame.groupby(..).std()`` with nullable integer dtype (:issue:`37415`)
 - Fixed regression in :class:`PeriodDtype` comparing both equal and unequal to its string representation (:issue:`37265`)
 - Fixed regression in certain offsets (:meth:`pd.offsets.Day() <pandas.tseries.offsets.Day>` and below) no longer being hashable (:issue:`37267`)
 
diff --git a/pandas/core/groupby/groupby.py b/pandas/core/groupby/groupby.py
index ab01f99ba11f9..4cf70db96e288 100644
--- a/pandas/core/groupby/groupby.py
+++ b/pandas/core/groupby/groupby.py
@@ -2573,9 +2573,9 @@ def _get_cythonized_result(
                     except TypeError as e:
                         error_msg = str(e)
                         continue
+                vals = vals.astype(cython_dtype, copy=False)
                 if needs_2d:
                     vals = vals.reshape((-1, 1))
-                vals = vals.astype(cython_dtype, copy=False)
                 func = partial(func, vals)
 
             func = partial(func, labels)
diff --git a/pandas/tests/groupby/aggregate/test_cython.py b/pandas/tests/groupby/aggregate/test_cython.py
index e01855c1b7761..c907391917ca8 100644
--- a/pandas/tests/groupby/aggregate/test_cython.py
+++ b/pandas/tests/groupby/aggregate/test_cython.py
@@ -277,3 +277,38 @@ def test_read_only_buffer_source_agg(agg):
     expected = df.copy().groupby(["species"]).agg({"sepal_length": agg})
 
     tm.assert_equal(result, expected)
+
+
+@pytest.mark.parametrize(
+    "op_name",
+    [
+        "count",
+        "sum",
+        "std",
+        "var",
+        "sem",
+        "mean",
+        "median",
+        "prod",
+        "min",
+        "max",
+    ],
+)
+def test_cython_agg_nullable_int(op_name):
+    # ensure that the cython-based aggregations don't fail for nullable dtype
+    # (eg https://github.com/pandas-dev/pandas/issues/37415)
+    df = DataFrame(
+        {
+            "A": ["A", "B"] * 5,
+            "B": pd.array([1, 2, 3, 4, 5, 6, 7, 8, 9, pd.NA], dtype="Int64"),
+        }
+    )
+    result = getattr(df.groupby("A")["B"], op_name)()
+    df2 = df.assign(B=df["B"].astype("float64"))
+    expected = getattr(df2.groupby("A")["B"], op_name)()
+
+    if op_name != "count":
+        # the result is not yet consistently using Int64/Float64 dtype,
+        # so for now just checking the values by casting to float
+        result = result.astype("float64")
+    tm.assert_series_equal(result, expected)