New York County is coterminous with the Borough of Manhattan, meaning all building permits are handled exclusively by the New York City Department of Buildings. There are no independent municipal building departments within the county, and all projects must comply with the NYC Zoning Resolution and specific flood zone requirements managed by the city.
How this fits with the state
The state authority here is Local licensing authorities; NYC DCWP / DOB in New York City. The county file does not replace that — it adds the permit office, local overlays, and the actual filing path.