You have 3 years from the fraud (or discovery of the fraud) to file a civil suit. For a criminal prosecution, the statute of limitations for a felony fraud is 4 years, and for a fraud that can only be prosecuted as a misdemeanor, the SOL would be 1 year.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
I am not sure which police department told you that the statute of limitations is three years for a criminal prosecution, however, that is incorrect. Under CA state law the statute of limitations for prosecution of a fraud crime is 4 years from the discovery of the crime, or within four years after the completion of the offense, whichever is later. The penal code section which provides this information is Section 801.5.
If you are still within this time frame you may want to contact the police again, or call the Los Angeles County District Attorney's Office.