Police say three suspects - two men and a woman - were seen on video last month and this month inside an apartment complex at 7th and Witmer Streets.
One of the suspects got into the building with a key fob and took the elevator to the second floor to the mailroom.
Detectives say he then used a counterfeit mailbox key to open mailboxes and take the mail.
He also has an electronic code to open the package locker and remove packages.
Anyone with information is urged to call Rampart Burglary Detective Elizabeth Holguin at (213) 484-3486. During non-business hours, or on weekends, calls should be directed to 1-877-LAPD-24-7 (877-527-3247). Anyone wishing to remain anonymous should call the LA Regional Crime Stoppers at 1-800-222-TIPS (800-222-8477) or go directly to www.lacrimestoppers.org.