Could a school district employee have a sex offender residing in their home?

I suggest you just go ask the school administration. I do not think this is an illegal act, but it could violate some school rule, or a term of your contract. I likely would need to read your teacher contract and the school board policy to give you a reliable answer. It would be much easier just to ask. Perhaps there is an ethics compliance officer in the district office, and your local school would never need to know you even asked. This answer also assumes your house is not disqualified under state law. (how close to a school, park, bus stop, play ground, etc.) The law is very restrictive in Ga. If so, your school could likely discharge you for violating the law on where sex offenders may reside. In GA, sex offenders must register. There is a web site where one may go and see where they all live. Many parents do this, so I would not question if they would even find out or not. Some parent is likely to see and report you. The offender likely has a probation officer that keeps up with where he/she lives, so it will not be a secret. Your question does not identify your state. This response is based on Georgia law. If you are in a state other than GA, resubmit your question, and identify your state. The laws likely are different in other states.

I would have to examine your contract with the school district to determine whether or not there were any such restrictions, but I doubt it. Generally the record of the person you're living with is not germane to your employment unless they are somehow involved.