An attorney for the 15-year-old girl filed the claim Friday, alleging Officer Robert Cain was improperly supervised.
The alleged abuse was discovered after a separate scandal involving cadets who were joyriding in police cars, using police equipment and even impersonating officers.
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Cain was believed to have been involved in helping the cadets check out the equipment from the department. The 10-year veteran officer worked as an equipment room operator.
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The teen cadet with whom Cain was suspected of having a sexual relationship was among the group of cadets arrested in connection with the police cruiser theft, LAPD Chief Charlie Beck said.
In a show of his seriousness in rooting out the source of the trouble, Beck personally put the cuffs on Cain when he was first arrested in June.
Prosecutors filed charges against the 31-year-old, including the illegal possession and manufacturing of assault rifles.
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Authorities seized a cache of nearly 100 illegal weapons from his Rancho Cucamonga home. The weapons included illegally modified assault rifles and other restricted firearms.