Addresses in cities or villages are assigned by the individual comunity. In cities you will contact the planning and zoning office. Usually village administrators assign addresses in villages.
Ashtabula County Community Services and Planning Office assigns addresses for 26 of the 27 townships in Ashtabula County. Only Ashtabula Township assigns its own addresses. Contact the zoning administrator for addresses in Ashtabula Township. In any other township contact the Ashtabula County Community Servicers and Planning Office. The application is available on the website.