Green’s Dictionary of Slang

an abbr. of SE pardon me.

1935		A. Kober Thunder over the Bronx 28: ‘You must parm me the forks,’ she apologized.
1939		W. Winchell On Broadway 9 Oct. [synd. col.] Parm me, but I got that wrong about Elizabeth Knaust.
1940		W. Winchell On Broadway 10 Apr. [synd. col.] Brenda Frazier stepped on his foot one night (and promptly said ‘Parm me)’.