Law Enforcement Officers Parity Act This bill expands the definition of law enforcement officer under provisions of the Federal Employees Retirement System (FERS) and the Civil Service Retirement System (CSRS). Specifically, the bill expands the definition to include (1) federal employees whose duties encompass the investigation or apprehension of suspected or convicted criminals and who are authorized to carry a firearm; (2) Internal Revenue Service employees whose duties are primarily the collection of delinquent taxes and the securing of delinquent returns; (3) U.S. Postal Inspection Service employees; (4) Department of Veterans Affairs police officers; and (5) certain U.S. Customs and Border Protection employees who are seized-property specialists with duties relating to custody, management, and disposition of seized and forfeited property. The bill deems service performed by an incumbent law enforcement officer on or after the enactment date of this bill to be service performed as a law enforcement officer for retirement purposes. The past service of such incumbents shall be treated as service performed by a law enforcement officer for retirement purposes only if a written election is submitted to the Office of Personnel Management within five years after the enactment of this bill or before separation from government service, whichever is earlier. An incumbent who makes an election before the enactment of this bill may pay a deposit into the Civil Service Retirement and Disability Fund to cover prior service. A law enforcement officer shall not be subject to mandatory separation during the three-year period beginning on the enactment of this bill.