All libraries in Kentucky are non-profit governmental units, operating as 170(c)(1)s. The IRS will deny public libraries the 501(c)(3) status. However, there are some grants that will only allow organizations with a 501(c)(3) status to apply. This is one reason that libraries frequently are supported by a Friends group with a 501(c)(3) status.
As a special service to government entities, IRS will issue a “government affirmation letter” free of charge. This letter describes government entity exemption from Federal income tax and cites applicable Internal Revenue Code sections pertaining to deductible contributions and income exclusion. Most organizations and individuals will accept the government affirmation letter as the substantiation they need.
Government entities can request a government affirmation letter by calling 1-877-829-5500.
More information may be found here: https://www.irs.gov/government-entities/federal-state-local-governments/governmental-information-letter
Also see the following pages: Friends of the Library Groups and Library Foundations, and Fundraising.