As can be seen in This posting on music copyright from OSU the copyright status under US law will depend on when the work was published. Works published before 1923 are generally in the public domain. Works published in or after 1923 but before 1964 will be under copyright unless the copyright was not renewed properly. Determining if a copyright was renewed is more than a bit tricky, and getting it wrong can expose a reuser to a lawsuit. work published in or after 1964 did not need to have the copyright renewed.
Works published before 1989 without a proper copyright notice may have entered the public domain, but again determining if this applies can be complicated and is at your own risk.
Note that the provisions on copyright renewal and copyright notice will often not apply if any author or co-author is not a US resident, or if the work was first published outside the US.
A brief musical quotation, or sampling or the like may constitute "fair use" under US law, but this can also be complex, and depends on the very specific facts of the case. That the use is not for profit does not automatically make it "fair use", although it may help a case for fair use.
If you can obtain permission from the copyright holder, this will remove all doubt and risk, and permission may be available for no more than a proper acknowledgement, depending on the work involved and how much you want to use.