diff --git a/pandas/_libs/tslibs/parsing.pyx b/pandas/_libs/tslibs/parsing.pyx
index 3da3d1e4b1b41..cef77f5a795af 100644
--- a/pandas/_libs/tslibs/parsing.pyx
+++ b/pandas/_libs/tslibs/parsing.pyx
@@ -251,10 +251,8 @@ def parse_time_string(arg, freq=None, dayfirst=None, yearfirst=None):
     -------
     datetime, datetime/dateutil.parser._result, str
     """
-    if not isinstance(arg, (str, unicode)):
-        # Note: cython recognizes `unicode` in both py2/py3, optimizes
-        # this check into a C call.
-        return arg
+    if not isinstance(arg, str):
+        raise TypeError("parse_time_string argument must be str")
 
     if getattr(freq, "_typ", None) == "dateoffset":
         freq = freq.rule_code
diff --git a/pandas/tests/indexes/period/test_period.py b/pandas/tests/indexes/period/test_period.py
index 8b3b66bd1ee6b..ac19fa70442cd 100644
--- a/pandas/tests/indexes/period/test_period.py
+++ b/pandas/tests/indexes/period/test_period.py
@@ -617,6 +617,44 @@ def test_insert(self):
             result = period_range("2017Q1", periods=4, freq="Q").insert(1, na)
             tm.assert_index_equal(result, expected)
 
+    @pytest.mark.parametrize(
+        "msg, key",
+        [
+            (r"Period\('2019', 'A-DEC'\), 'foo', 'bar'", (Period(2019), "foo", "bar")),
+            (r"Period\('2019', 'A-DEC'\), 'y1', 'bar'", (Period(2019), "y1", "bar")),
+            (r"Period\('2019', 'A-DEC'\), 'foo', 'z1'", (Period(2019), "foo", "z1")),
+            (
+                r"Period\('2018', 'A-DEC'\), Period\('2016', 'A-DEC'\), 'bar'",
+                (Period(2018), Period(2016), "bar"),
+            ),
+            (r"Period\('2018', 'A-DEC'\), 'foo', 'y1'", (Period(2018), "foo", "y1")),
+            (
+                r"Period\('2017', 'A-DEC'\), 'foo', Period\('2015', 'A-DEC'\)",
+                (Period(2017), "foo", Period(2015)),
+            ),
+            (r"Period\('2017', 'A-DEC'\), 'z1', 'bar'", (Period(2017), "z1", "bar")),
+        ],
+    )
+    def test_contains_raise_error_if_period_index_is_in_multi_index(self, msg, key):
+        # issue 20684
+        """
+        parse_time_string return parameter if type not matched.
+        PeriodIndex.get_loc takes returned value from parse_time_string as a tuple.
+        If first argument is Period and a tuple has 3 items,
+        process go on not raise exception
+        """
+        df = DataFrame(
+            {
+                "A": [Period(2019), "x1", "x2"],
+                "B": [Period(2018), Period(2016), "y1"],
+                "C": [Period(2017), "z1", Period(2015)],
+                "V1": [1, 2, 3],
+                "V2": [10, 20, 30],
+            }
+        ).set_index(["A", "B", "C"])
+        with pytest.raises(KeyError, match=msg):
+            df.loc[key]
+
 
 def test_maybe_convert_timedelta():
     pi = PeriodIndex(["2000", "2001"], freq="D")
diff --git a/pandas/tests/tslibs/test_parsing.py b/pandas/tests/tslibs/test_parsing.py
index 126a1bd12ad59..7df7dbbf91d0b 100644
--- a/pandas/tests/tslibs/test_parsing.py
+++ b/pandas/tests/tslibs/test_parsing.py
@@ -209,3 +209,13 @@ def test_try_parse_dates():
 
     expected = np.array([parse(d, dayfirst=True) for d in arr])
     tm.assert_numpy_array_equal(result, expected)
+
+
+def test_parse_time_string_check_instance_type_raise_exception():
+    # issue 20684
+    with pytest.raises(TypeError):
+        parse_time_string((1, 2, 3))
+
+    result = parse_time_string("2019")
+    expected = (datetime(2019, 1, 1), datetime(2019, 1, 1), "year")
+    assert result == expected