PUBLIC FUNDS IN GENERAL
PUBLIC DEPOSITORY LAW
57-128. DESIGNATION OF DEPOSITORY. The supervising board shall designate one or more financial institutions within the boundaries of the depositing unit which are qualified public depositories as defined by section 57-110, Idaho Code, and which is in compliance with section 57-113, Idaho Code, as depository or depositories for the moneys required to be kept by the treasurer. Such designation shall be determined by competitive bidding or by other means generally accepted as standard business practice. In no case shall the deposit or deposits of public funds of any depositing unit in any public depository, exceed at any one (1) time in the aggregate the total of the capital and surplus or reserves and unallocated or undivided earnings, as applicable, of such public depository. In the event that any financial institution has been designated as a depository under this chapter, such designation shall continue in force until revoked by the supervising board of the depositing unit.
Now the process only has to be done when a new designated depository is chosen and stays in effect until the supervising board, in this case the City Council, revokes the depository.
Anyway for those that are interested, that's how it works.