In all counties not having a county election commissioner, the expense of printing and distributing ballots and all other expenses connected with and that are necessary to provide for national, state, county, township, city and school primary and general elections shall be paid by the county. Expenses connected with registration and copies of registration lists by cities of the first and second classes shall be paid by such cities. Whenever it is provided by law that certain election expenses shall be paid or reimbursed by any city, school district, community junior college district or any public special district, this section shall not be construed to prevent such reimbursement.