There seems to be a trend for libraries that have Friends groups to hold fundraisers, donations, and membership drives at the library. In some instances, the library collects money for the Friends and pays it to them at a later date.
Ideally, a public library does NOT handle the money of another entity, even for "Friends." Ever.
That said, there is no law barring a library from helping out a partner or organization with cash handling for events; this "never" rule comes from risk management, not the law.