(2) can you also answer the question as if the police union is not a 501(c)(3)?
(3) does it matter that I don't live in the city or state where the police union is located and where the police officer who got shot was serving? In other words, do I only get a charitable deduction if it's for my own police department?
Donations are tax deductible if made to an exempt organization or to a branch of government. (A police union or PBA is not a branch of gov't so that doesn't apply.) Not all exempt organizations are 501(c)(3) organization. You can look up any organization on the IRS Select Check web site. https://www.irs.gov/charities-non-profits/exempt-organizations-select-check
A donation to an exempt organization to be used as the organization sees fit, is tax-deductible, and you don't have to be concerned with how the organization uses the funds.
Donations to specific individuals are never deductible, even if the person is needy, or if the donation is managed by an exempt organization (and the organization can get in big trouble for issuing donation receipts for such donations). This generally means that if the PBA collects donations for "the family of officer Smith", you can't deduct that. But if the organization collects donations for "a fund for the families of officers killed in the line of duty", and the decision of which families qualify for the donations is made by the organization and not directed by the donors, that will generally be an allowable deduction.
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