A board of park commissioners may provide for employees’ pensions pursuant to an authorized city pension plan with the consent of the city governing body and the consent of not less than a majority of the city employees covered by the city pension plan. In addition, a board of park commissioners may provide for employer pensions pursuant to chapter 54-52 or under a program approved by the internal revenue service. Payments made by employees or taxes levied by the park district must be paid into the employees’ pension fund. If a board of park commissioners wishes to leave an existing city pension plan, the board, upon the request of the pension fund governing body, shall fund an actuarial study of the financial impacts to the pension fund. Any losses or costs to the fund by the park district leaving the pension plan are the responsibility of the park district. A park district may not leave the city’s pension plan without the approval of the pension fund governing body.