diff --git a/pandas/tests/scalar/period/test_period.py b/pandas/tests/scalar/period/test_period.py
index 795021a260028..5006e16b6a7e0 100644
--- a/pandas/tests/scalar/period/test_period.py
+++ b/pandas/tests/scalar/period/test_period.py
@@ -6,6 +6,7 @@
 
 from pandas._libs.tslibs import iNaT, period as libperiod
 from pandas._libs.tslibs.ccalendar import DAYS, MONTHS
+from pandas._libs.tslibs.np_datetime import OutOfBoundsDatetime
 from pandas._libs.tslibs.parsing import DateParseError
 from pandas._libs.tslibs.period import INVALID_FREQ_ERR_MSG, IncompatibleFrequency
 from pandas._libs.tslibs.timezones import dateutil_gettz, maybe_get_tz
@@ -776,6 +777,35 @@ def test_period_deprecated_freq(self):
             assert isinstance(p1, Period)
             assert isinstance(p2, Period)
 
+    def _period_constructor(bound, offset):
+        return Period(
+            year=bound.year,
+            month=bound.month,
+            day=bound.day,
+            hour=bound.hour,
+            minute=bound.minute,
+            second=bound.second + offset,
+            freq="us",
+        )
+
+    @pytest.mark.parametrize("bound, offset", [(Timestamp.min, -1), (Timestamp.max, 1)])
+    @pytest.mark.parametrize("period_property", ["start_time", "end_time"])
+    def test_outter_bounds_start_and_end_time(self, bound, offset, period_property):
+        # GH #13346
+        period = TestPeriodProperties._period_constructor(bound, offset)
+        with pytest.raises(OutOfBoundsDatetime, match="Out of bounds nanosecond"):
+            getattr(period, period_property)
+
+    @pytest.mark.parametrize("bound, offset", [(Timestamp.min, -1), (Timestamp.max, 1)])
+    @pytest.mark.parametrize("period_property", ["start_time", "end_time"])
+    def test_inner_bounds_start_and_end_time(self, bound, offset, period_property):
+        # GH #13346
+        period = TestPeriodProperties._period_constructor(bound, -offset)
+        expected = period.to_timestamp().round(freq="S")
+        assert getattr(period, period_property).round(freq="S") == expected
+        expected = (bound - offset * Timedelta(1, unit="S")).floor("S")
+        assert getattr(period, period_property).floor("S") == expected
+
     def test_start_time(self):
         freq_lst = ["A", "Q", "M", "D", "H", "T", "S"]
         xp = datetime(2012, 1, 1)