The expenses of the recount of the votes as provided in this article, if for an office to be filled by state electors, or if upon an initiative or referendum measure, or proposal to amend the constitution, shall be a state charge, and if for an office to be filled by the electors of a county or a subdivision of a county, or precinct, shall be a county charge. In the case of an office to be filled by the electors of a city or town, the expenses of the recount shall be a city or town charge.