THE DA CLAIMS CHRIS BROWN LIED ABOUT COMMUNITY SERVICE & VIOLATED HIS PROBATION!

The L.A. County District Attorney has filed legal documents claiming Chris Brown has violated his probation by submitting bogus community service records ... claiming in one case he swore he was picking up trash in Virginia when he was actually on a PRIVATE JET TO CANCUN.

We've learned the D.A. is alleging in legal docs Chris Brown may have LIED when he claimed he had performed all of his community service in connection with the Rihanna beating case.

Bryan T. Norwood, the Chief of Police in Richmond, VA., wrote a letter to the judge on September 14, claiming Brown successfully completed 202 days of community service -- he was only required to perform 180.

Norwood attached documents showing that Brown frequently worked at Tappahannock Children's Center -- a place where Brown's mom was once a director -- and did odd jobs such as painting, washing windows, waxing floors, cutting grass and picking up trash.

According to legal docs obtained by TMZ ... the Richmond P.D. admits they only supervised Brown on 9 or 10 occasions and on all other dates he was not supervised by anyone.

And get this ... the detective who had been assigned to oversee Brown's community service was told she did not have to continue monitoring at the Children's Center. The times, location and types of duty were provided by Chris Brown's mother.

The D.A. claims Chris and the Chief of Police had a prior relationship.

And there's more. According to the docs, Chris' lawyer, Mark Geragos, "instructed" the lawyer for the Richmond P.D. on how to "handle" D.A. investigators' questions about Chris' community service.

And Geragos told the probation officer there was a court order that Chris' community service be removed from the probation department and given to the police chief. Fact is ... there was no such court order.

Pretty ironic -- during a progress hearing back in November, Geragos brazenly said the prosecutor had a "doubting attitude" for questioning a probation report which said Brown had met all his terms and conditions.

And there's more ... the Administrator of the Children's Center allegedly tried coaching the floor waxing guy on what to say to D.A. investigators, but he refused to lie and in fact had already told investigators he was the only one who waxed the floors for the past 3 years. Chris claimed in docs he waxed the floors on some occasions.

The judge was suspicious when the community service documents were filed, and sources tell us the D.A. began investigating and found no "credible, competent or verifiable evidence" that Brown did the 180 days community service.

Sources tell TMZ ... there's no way Chris could have performed community service on some of the days, because he was out of the country doing concerts.

The D.A. calls Chris' documentation "at best sloppy ... and at worst fraudulent reporting."

The D.A. is asking the judge to reject Chris' alleged Virginia community service hours and make him fulfill his obligation in L.A. County.

By the way, the D.A. claims Chris' mom was responsible for orchestrating work at the Children's Center outside of normal operating hours and a key administrator told the D.A. she NEVER saw Chris perform any work at the center.

And the D.A. is also saying there are other possible probation violations, including:

-- The Frank Ocean fight at the recording studio
-- Brown testing positive for pot
-- Failing to obtain a travel permit
-- Allegedly grabbing and throwing a fan's phone in Miami
-- Throwing a chair through a window at "Good Morning America"

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