Does the county payment to a municipal library for library services provided to non-residents of the municipality go to the library or the municipality’s general fund?

The payment goes to the library. Under Wis. Stat. 43.12(1), a county that does not maintain a consolidated public library for the county under sec. 43.57 and that contains residents who are not residents of a municipality that maintains a public library under secs. 43.52 or 43.53 must pay to each public library in the county and to each public library in an adjacent county, other than a county with a population of at least 500,000, an amount based on a statutory formula.  The statute indicates that the payment is to the public library.  The county payment must be made to the library, either directly or to the library system which then pays the library. The check must then be deposited with the municipality in a fund under library board control.