Let's use np.logical_and:

import numpy as np
import pandas as pd
df = pd.DataFrame({'A':[True, True, False, True, np.nan, np.nan], 
                   'B':[True, False, True, np.nan, np.nan, False]})

s = np.logical_and(df['A'],df['B'])
print(s)

Output:

0     True
1    False
2    False
3      NaN
4      NaN
5    False
Name: A, dtype: object

pandas >= 1.0

This operation is directly supported by pandas provided you are using the new Nullable Boolean Type boolean (not to be confused with the traditional numpy bool type).

# Setup
df = pd.DataFrame({'A':[True, True, False, True, np.nan, np.nan], 
                   'B':[True, False, True, np.nan, np.nan, False]})

df.dtypes                                                                  

A    object
B    object
dtype: object

# A little shortcut to convert the data type to `boolean`
df2 = df.convert_dtypes()                                                  
df2.dtypes                                                                 

A    boolean
B    boolean
dtype: object

df2['A'] & df2['B']                                                        

0     True
1    False
2    False
3     <NA>
4     <NA>
5    False
dtype: boolean

In conclusion, please consider upgrading to pandas 1.0 :-)