Green’s Dictionary of Slang

shag n.2

[shag v.2 (2)]

(US tramp) a chase, a hue and cry; a ‘tail’.

[US]Irwin Amer. Tramp and Und. Sl. 167: Shag.–A chase or organized pursuit by the police or by an irate citizenry.
[US]C.S. Montanye ‘Crepe for Suzette’ Thrilling Detective Oct. [Internet] When Mullin thought I was chiseling on the police he had a habit of sticking a shag on me [...] But nobody tailed me to Broadway.
[US]Ragen & Finston World’s Toughest Prison 817: shag – A chase or organized pursuit by the police or an irate citizenry.