Ah...the age old war between cat people and dog people...
I imagine the laws are different for every state, county or whatever, but you should be able to contact animal control in your area and get a written copy of whatever laws are enforcable in your area.
Your best options in the long run are to do whatever is necessary to ensure your dog doesn't escape when you aren't home (maybe look into a pet sitter to come by a few times during the day to check on him and play with him so he doesn't get so lonely) and to try and make peace with your neighbors so they don't view you and your dog as neighborhood nuisances that must be reported for every infraction.
Training for you and your puppy is essential...dogs love to chase anything moving and a dog running free can terrorize a nervous child who is trying to escape it, even if no actual harm ensues. Beagles are adorable, but they were actually rated in the top 10 for aggression, so it's possible your puppy was frightening the child.
The bottom line is...you are responsible for everything your dog does, so the only way to protect yourself and your dog from (possibly unfair) repercussions is to do whatever is necessary to prevent the kinds of situations where trouble can occur. It is up to you to keep him on your property or under your control at all times. You can't defend against actions that occur when you aren't there to witness them, and as long as your dog has the ability to escape your control, you (and he) will be at risk, not just from situations like this, but he is also at risk of being lost, stolen, injured or even killed while he is running free.
Count yourself lucky that it wasn't worse...that the child wasn't really harmed and that your dog is safe...learn from the experience and do what it takes to protect your puppy from a repeat performance.