diff --git a/xarray/tests/test_cftimeindex.py b/xarray/tests/test_cftimeindex.py
index f6eb15fa373..23e66e1ad83 100644
--- a/xarray/tests/test_cftimeindex.py
+++ b/xarray/tests/test_cftimeindex.py
@@ -988,6 +988,30 @@ def test_cftimeindex_calendar_property(calendar, expected):
     assert index.calendar == expected
 
 
+def test_cftime_noleap_with_str():
+    time=xr.cftime_range('2000-01-01','2006-01-01', freq='D', calendar='noleap')
+    temperature =  np.ones(len(time))
+    da = xr.DataArray(
+        data=temperature,
+        dims=["time"],
+        coords=dict(time=time,),
+    )
+    out=da.sel(time=slice('2001','2002'))  # works if array is built with cftime
+    da1=da.convert_calendar('noleap')
+    out1=da1.sel(time=slice('2001','2002'))  # works if array is built with cftime and converted
+
+    time=pd.date_range('2000-01-01','2006-01-01', freq='D',)
+    temperature =  np.ones(len(time))
+    da2 = xr.DataArray(
+        data=temperature,
+        dims=["time"],
+        coords=dict(time=time,),
+    )
+    out2=da2.sel(time=slice('2001','2002')) #  # works if array is built with pandas time
+    da3=da2.convert_calendar('noleap')
+    out3=da3.sel(time=slice('2001','2002')) # fails if array is built with pandas time and convert to noleap
+
+
 @requires_cftime
 def test_empty_cftimeindex_calendar_property():
     index = CFTimeIndex([])