The petition or complaint shall be in the name of the state and may be filed upon the relation of the attorney general and reporter, or the district attorney general for the state, or the county attorney in the case of county officers, and of the city attorney, or the district attorney general, in the case of municipal officers; and in all cases it may be filed, without the concurrence of any of such officers, upon the relation of ten (10) or more citizens and freeholders of the state, county, or city, as the case may be, upon their giving the usual security for costs.