Green’s Dictionary of Slang

tilly n.3

also Tilly law, Tilly Tight-twat
[the use of a woman’s name to ‘feminize’ the force]

(gay) the police.

[US]Lavender Lex. n.p.: tilly:– The beat, cop.
[US]B. Rodgers Queens’ Vernacular 126: the police [...] Tilly [Tight-twat] (camp, mid-late ’60s, because he runs a tight ship and keeps a tight asshole).
[US]Russo ‘Camp’ in Levine Gay Men (1979) 206: Police become ‘Alice blue gown’ or ‘Tillie law.’.
[NZ](con. 1960s) W. Ings ‘Trolling the Beat to Working the Soob’ in Int’l Jrnl Lexicog. 23:1 72: In the early 1960s in New Zealand Vivian Vice, Nelly-law, Dolly Handbag, Alice, Dora-D, Hilda-Handcuff, Lily-lunchbox, Jennifer-Justice, Hilda Box-rot, Petunia Pig, Tilly Tight-twat, and Cherie Cunstable, were familiar.