All claims that may arise in connection with the transportation authority shall be presented as ordinary claims against a common carrier of passengers for hire: Provided, That written notice of any claim based upon injury to persons or property shall be served upon the authority no later than 60 days from the occurrence through which such injury is sustained and the disposition thereof shall rest in the discretion of the authority and all claims that may be allowed and final judgment obtained shall be liquidated from funds of the authority: Provided, further, That only the courts situated in the counties in which the authority principally carries on its function are the proper counties in which to commence and try action against the authority.