The city’s effort to repurpose the former Meriden-Wallingford Hospital inched forward this past week, with the City Council’s Finance Committee signing off on a request to pursue state grant funds to partially demolish the site. The Finance Committee on Tuesday approved a request by city officials to apply for state funding through the Connecticut Communities Challenge Grant program, which is administered by the state Department of Economic and Community Development. The request must still be adopted by the whole City Council, which meets Monday. The application deadline is Oct. 7. City officials have proposed a roughly $6 million project to demolish the main hospital building, while potentially leaving the former nurses hospital building and parking garage intact. The city could pursue a scaled down demolition should officials with the State Historic Preservation Office decide the nurses portion must be preserved.