Maya Rudolph's Baby -- Birth Details Kept Secret For A Year!!

Maya Rudolph just filed the birth certificate for her baby -- which is interesting because she gave birth A YEAR AGO.

According to to the document -- obtained by TMZ -- Maya and longtime partner Paul Thomas Anderson gave birth to a baby girl on Aug. 1, 2013 ... naming her Minnie Ida Anderson after Maya's mother, Minnie Riperton.

Everything was pretty much on the down low until the certificate was filed Tuesday in L.A. The reason -- Maya gave birth at home, so there was no hospital to record the birth.

In California ... birth certificates must be filed before the baby turns 1, so Maya and Paul got in just under the wire.

Happy birthday, Minnie!