Copyright laws about historical sound recordings*
There is no federal copyright for sound recordings made before Feb. 15, 1972. Currently, copyright laws for sound recordings are determined individually by states, but distributing recordings in a state where it's legal to do so doesn't protect you if your users reside in states where it's illegal. It's a big mess. Currently, the soonest sound recordings may enter the public domain is 2067. I'll forgive you if you're unwilling to wait.

If you have access to recordings, and want to share that access with others, you aren't without options. Copyright expert Peter Hirtle recommends practicing risk assessment, not allowing 'fear, uncertainty and doubt' to prevent us from sharing, learning and listening. In short, know your rights.

Risk assessment is the practice of asking "who am I likely to offend by distributing this material" and "what action are they allowed to, and, importantly, likely to take against me". This can be subject to many different factors, but I'll break down some common cases in order of increasing legal risk.
  • Transfers of noncommercial recordings
  • Transfers of commercial cylinders and 78s
  • Transfers of reissue LPs published by defunct record companies
  • Transfers of out-of-print reissue LPs by extant record companies
  • Recordings that are available for sale in their original, or updated (CD, mp3) format
Please don't do the last activity in this list!! Reissue labels spend immense amounts of time and money finding recordings that are suitable for reissue, and giving these recordings away undermines their market and decreases the resources they can spend continuing to provide access.

The second to last is a situation I work with frequently. It's a grey area, in my opinion, but I tend toward distributing because I think access is more important than profit (and if they aren't selling them, there's no "statutory damage" (i.e. opportunity cost)). At the same time, for better or worse, it's hard to limit the spread of recordings once they've gone digital. Proceed with caution.

I treat out of print cylinders, 78rpm records, and defunct-publishers' reissue LPs as 'orphan works'. Even if rightsholders may hypothetically exist somewhere, I believe we have a right to use and distribute these recordings if the original composers, performers or recording staff are no longer benefiting from the royalties.

The first option presents little legal risk, but it's good practice to ask contributors whether they're okay with whatever use you have in mind.

Finally, familiarize yourself with the doctrine of fair use, especially if you work for an educational institution. Fair use provides for the legal, unauthorized use of portions of copyrighted material for study and teaching. Peter Hirtle has written a checklist that may help you decide whether a way you intend to use a recording falls under this practice.

Some ways to avoid a suit:
  • Don't charge for access. Note that recordings are for education and entertainment purposes only
  • Distribute only recordings that are unavailable commercially
  • Use a disclaimer that states that recordings are provided under an assertion of fair use, and that requests to credit rightsholders or remove recordings will be honored
  • If you think an item is still under copyright, a well documented search for the rights holder may be in your best interest

Copyright violations can be extremely costly in the form of damages paid to the rightsholder, and representation in court. Hiring an attorney to asses your practice may save you a costly and embarrassing court battle. A 'cease and desist' letter is more likely than a lawsuit for recordings distributed in good faith of purpose.

* I am not a lawyer or a copyright professional. Any information here is for educational purpose only, and is not to be considered professional legal advice. Consult a lawyer if you need a professional opinion for a specific application.