From discussion in #15589, the handling of NaT is different for different datetime fields.
On a scalar value, is_leap_year returns False, the others are not defined:
In [1]: pd.Timestamp('NaT').is_month_start
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
<ipython-input-1-654cc4e613aa> in <module>()
----> 1 pd.Timestamp('NaT').is_month_start
AttributeError: 'NaTType' object has no attribute 'is_month_start'
In [2]: pd.Timestamp('NaT').is_leap_year
Out[2]: False
On an index (or series .dt accessor), is_leap_year returns False, the others propagate NaN (with the consequence it is no longer a boolean array/series):
In [3]: pd.DatetimeIndex(['2012-01-01', 'NaT']).is_month_start
Out[3]: array([ 1., nan])
In [4]: pd.DatetimeIndex(['2012-01-01', 'NaT']).is_leap_year
Out[4]: array([ True, False], dtype=bool)
So when is_leap_year was introduced in #13739, this was done on purpose, citing @sinhrks "pd.NaT.is_leap_year results in False, as I think users want bool array.".
This seems indeed the more logical thing to return (certainly for arrays/series), so you can eg use it for indexing. For scalars it is a bit less clear what is the preferable option (return False or NaN), but probably best to be consistent.
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