The Cassell Dictionary of Slang
1 [late 19C+] (orig. US theatrical] to make oneself attractive to a member of the opposite sex, to flirt with, to succeed in seduction; thus "mashing", seducing, making advances (cf. MASHED adj.)
2 [1950s] (W.I) to seduce, to rape (cf. MASH THE FAT)
3 [1980s+] (US campus) to kiss, to neck [? SE "mash", to crush, to pulp, thus to render 'soft', note Rom. "mash", to allure, to entice]
Lighter, Historical Dictionary of American Slang
1. to assault; beat up; (occ.) to kill
2. to flirt with or make romantic advances toward; (also) (all obs.) to caus to be romtantically smitten; succeed in romancing; seduce. -- also (ob.s) used intras. or absol.
1877 Puck (May) 3: Lester Wallack, Edwin Booth, and Montague [could] earn a respectable living ... blacking the shoes of the young ladies they've succeeded in "mashing" [...]
3. Black E. to give; LAY ON. -- also constr. with "on"
4. Stu. to kiss and hug; MAKE OUT, 2.b.
1986 Univ. Tenn. student theme: "Mashing" and "grubbing" [are] the current synonyms for making out.
1996 Mystery Sci. Theater (Comedy Central TV): Should we start mashin' now?
After getting off my lazy read end and consulting some dictionaries, it seems that "mash" may even originate in AE! The citations given in Lighter seem to suggest that "to mash" in the sense "to flirt" may have fallen out of use in the 1930s, and that the sense "to make out", "to neck" may be the one currently in use.
Any native speakers care to weigh in?