A quick look on Google ("film" followed by "Arsenic and Old Lace" throws up a play: "Arsenic and Old Lace is director Frank Capra's spin on the classic Joseph Kesselring stage comedy". But I haven't the time to see if the play came from a book. shaneystar2's suggestion looks interesting, though.
I think my answer was way off !
I did find this--Arsenic and Old Lace - (1944-Black&White) - Film.Based on a book that was based on the Vera Renzi murders. So..if you can find that book that could be the answer..!