William O'Dwyer was elected NYC mayor in 1945.  Before that, he was
the Brooklyn district attorney through 1941.

What did he do in the years in between?

O'Dwyer enlisted in the US Army in 1941, and served until his military
retirement in 1945.

From the official New York City Web site:

"O'Dwyer built up a successful law practice and served as a Kings
County Court judge. He won election as the Kings County District
Attorney in 1939 and his prosecution of the organized crime syndicate,
Murder, Inc., made him a national celebrity as a tough crime fighter.
After losing the election to LaGuardia in 1941, O'Dwyer enlisted in
the Army, achieving the rank of brigadier general."

Elected Mayors of New York City 
http://www.nyc.gov/html/nyc100/html/classroom/hist_info/mayors.html

"O'Dwyer 
 William, Brigadier-General 

(1890-1964) 

1945 Retired
1946 - 1950 Mayor of New York
1950 - 1952 Ambassador to Mexico"

The Generals of WWII: Generals from USA
http://www.generals.dk/general/O'Dwyer/William/USA.html

My Google search strategy:

Google Web Search: "william o'dwyer" mayor 1941
://www.google.com/search?hl=en&q=%22william+o%27dwyer%22+mayor+1941

I hope this is precisely what you need to know. If anything is unclear
or incomplete, please request clarification; I'll gladly offer further
assistance before you rate my answer.

Best regards,
pinkfreud