Harrison was known as the most reclusive Beatle
The former Beatle died on 29 November from lung cancer, apparently at the Los Angeles home of friend and security consultant Gavin de Becker.
But the official death certificate lists a different address, which postal authorities have since said does not appear to exist.
The exact site of celebrity deaths is sometimes obscured to try to prevent the place of death becoming a shrine or a place pilgrimage for fans.
'Privacy'
Lawyer Gloria Allred has said that she lodged the complaint with Los Angeles police because she was concerned that the "integrity of public records is at stake".
"Celebrities and/or their supporters are not above the law, even if they are acting with good intentions, for example, to protect the privacy of loved ones," she said.
"All things must pass, but not this," she added.
On Wednesday a Los Angeles police spokesman said that no one had been charged with any offence over the address on the certificate.
Information
The spokesman said it was not a crime to give a different address as the place of death - unless there was an intent to defraud, for example with regard to life insurance.
Harrison, 58, was known as the most reclusive of the Beatles, and detailed information about his death has been scarce.
The media were not informed of his death until the day after it occurred, and mystery has surrounded reports that his ashes were to be scattered in the Ganges river.
Despite intense fan and media interest, the reports were eventually dismissed by Indian police as speculation.