Not sure if this is quite what you're thinking about when you're referring to "deputizing", but I just found the section of California's statutes regarding posse comitatus:

Section 150 of the California penal code

150. Every able-bodied person above 18 years of age who neglects or refuses to join the posse comitatus or power of the county, by neglecting or refusing to aid and assist in taking or arresting any person against whom there may be issued any process, or by neglecting to aid and assist in retaking any person who, after being arrested or confined, may have escaped from arrest or imprisonment, or by neglecting or refusing to aid and assist in preventing any breach of the peace, or the commission of any criminal offense, being thereto lawfully required by any uniformed peace officer, or by any peace officer who identifies himself or herself with a badge or identification card issued by the officer's employing agency, or by any judge, is punishable by a fine of not less than fifty dollars ($50) nor more than one thousand dollars ($1,000).

The wording sounds fairly broad. Sounds like you could deputize civillians to do anything from: serve an arrest warrant, to help chase an escaped prisoner, to help quell a riot, and maybe patrol a neighborhood to prevent looting, etc. Hmmm, or if an officer is wrestling with a suspect and asks a bystander for help to subdue the person, I guess the LEO is technically invoking posse comitatus on the civillian. I had never thought of it that way until now.

Anyway, hope that helps. And I am not a lawyer nor an LEO, nor do I play one on TV.