diff --git a/ci/code_checks.sh b/ci/code_checks.sh
index 9aae477ca1af3..04e66d9bf3603 100755
--- a/ci/code_checks.sh
+++ b/ci/code_checks.sh
@@ -100,7 +100,6 @@ if [[ -z "$CHECK" || "$CHECK" == "docstrings" ]]; then
         -i "pandas.DataFrame.var PR01,RT03,SA01" \
         -i "pandas.DatetimeIndex.indexer_at_time PR01,RT03" \
         -i "pandas.DatetimeIndex.snap PR01,RT03" \
-        -i "pandas.DatetimeIndex.std PR01,RT03" \
         -i "pandas.DatetimeIndex.to_period RT03" \
         -i "pandas.DatetimeIndex.to_pydatetime RT03,SA01" \
         -i "pandas.DatetimeTZDtype SA01" \
diff --git a/pandas/core/arrays/datetimes.py b/pandas/core/arrays/datetimes.py
index 106064ade8344..0f59d62339bf2 100644
--- a/pandas/core/arrays/datetimes.py
+++ b/pandas/core/arrays/datetimes.py
@@ -2248,9 +2248,25 @@ def std(
         axis : int, optional
             Axis for the function to be applied on. For :class:`pandas.Series`
             this parameter is unused and defaults to ``None``.
+        dtype : dtype, optional, default None
+            Type to use in computing the standard deviation. For arrays of
+            integer type the default is float64, for arrays of float types
+            it is the same as the array type.
+        out : ndarray, optional, default None
+            Alternative output array in which to place the result. It must have
+            the same shape as the expected output but the type (of the
+            calculated values) will be cast if necessary.
         ddof : int, default 1
             Degrees of Freedom. The divisor used in calculations is `N - ddof`,
             where `N` represents the number of elements.
+        keepdims : bool, optional
+            If this is set to True, the axes which are reduced are left in the
+            result as dimensions with size one. With this option, the result
+            will broadcast correctly against the input array. If the default
+            value is passed, then keepdims will not be passed through to the
+            std method of sub-classes of ndarray, however any non-default value
+            will be. If the sub-class method does not implement keepdims any
+            exceptions will be raised.
         skipna : bool, default True
             Exclude NA/null values. If an entire row/column is ``NA``, the result
             will be ``NA``.
@@ -2258,6 +2274,7 @@ def std(
         Returns
         -------
         Timedelta
+            Standard deviation over requested axis.
 
         See Also
         --------