We are about to release a new app in Beta version to a limited number of users. We rely on them to give us final verification and feedback on the app, and later to be ambassadors of the final release. Should we consider a formal, legal agreement with these users that specifies things like: -no redistribution -no transfer of ownership -anything else?
Unless your application is something you'd have to submit through the FDA or other regulatory because its use could impact health, all you should need are disclaimers. You aren't giving the person source code. You are asking them to take time from their schedules to try out your offering and to give you feedback that will hopefully help you to shape a product that is of more value and that users will want to use. It's not a final application and unless it's extremely high value per unit (1M / unit) it's not a true product, you're not losing any customers even if they give it to someone else, you're simply getting someone else to give feedback on your product. If you're worried about someone copying it, unless you're at the forefront of a very competitive industry, where a competitor will put a lot of engineers on copying and improving what you have immediately, there's no need to worry about your app being disseminated by users. If you don't want more user feedback, you can ask your users to not distribute it. And then you can ignore if someone else gives you feedback beyond the limited beta.
You can find typical disclaimers that you include with your product by looking at commercial product. This essentially states that people are aware that this is not final product, their data is not safe, they should back it up, that the product will have bugs, and that they are offered it so you can get feedback to improve your product.
I don't know your product so cannot guess beyond this as to other potential issues that might make you ask the question above. Please feel free to give me a call to discuss if you would like to go into this in more detail.