Bingo is a highly regulated industry. In Texas, a state permit is required for a non-profit to hold a bingo game. It requires a fair amount of paperwork (which isn't so bad after the first filing) and $25 fee per game, with a maximum of 6 per year.
Everyone working the game and all the Board members undergo background checks as part of the application process.
Our PTO dutifully follows the rules and gets our license each year. However, I find it a bit much that in our state, you need a license to run ANY bingo game - even if it's free!
Normally, I'm not one to ignore rules or laws, but if we WERE planning a free game just for fun with no money involved, I can't say we'd go through the paperwork.
Yes, you can do it. We have looked into it because it is something we have wanted to do for a while. It varies by state, but typically you need a liscense from your town and a liscense from the state. Because you are non-profit, the liscensing fess are rather low.
Go to your town hall and ask them what you need. Like Melloweer stated you need to check with your state gamming commision too. I was able to get the state info online. Your state info should also be available online. Your town hall should also be able to direct you.