Insulate ceiling

[coztello]

Hi,
I have removed the old ceiling in the house we recently bought. As you can see in the pictures, the ceiling is partially insulated and has a vapor barrier installed. I plan to remove all the old insulation, add furring strips, insulate, and install a new ceiling (after the electrician has come and installed some wiring).
Now to my question: Is a vapor barrier necessary? The ceiling is not the outer roof, as we have another floor in the house.

Thanks for your answer.

Regards,
Coz