Green’s Dictionary of Slang

(Aus. Und.) to make a written confession.

1975		Bulletin (Sydney) 26 Apr. 45: The detective had suggested to Pig that he sign up (confess and make a signed written statement) regarding the matters and then plead guilty.
1990		Tupper & Wortley Aus. Prison Sl. Gloss. 🌐 Sign up. To inform upon another prisoner. Derives from the actual signing of a record of interview with police where others have been implicated.