Can the other person still file an insurance claim against me if I wasn't issued a citation?
I was in an accident and I was at-fault. But I was never given a citation. Can the other person still file a claim without one?
Yes, regardless of police involvement the other party can file a claim against you if you were at-fault. Your insurance will want to settle the claim to avoid a lawsuit. If they payout, it will be marked on your record as a claim paid.
If you have any questions, feel free to ask.