If a child ran out into the street and I hit him, am I at fault?

The rain, time of night and what you were doing all play into the factors of whether or not you would be held liable criminally and or civilly for hitting a child. At 9:30pm, what is a minor doing out in the middle of the street without adult supervision is what you need to use as your leading point. Did you talk to the officer and was there a police report prepared? If so, then you need to order the police report or get a copy from your insurance company and find out if a claim has been filed against you. It appears you were not arrested for any sort of negligent driving so it may appear you won't be held at fault. You need to look at the police officer report and see if there is blame mentioned or if the report pretty much blames the child. You need to ask the insurance company if your policy covers it to hire a lawyer to defend the claim if a lawsuit is filed (usually filed against both you and the insurance company because of the deep pocket idea) and you need to write everything down as you remember it immediately and have it notarized with a time and day because it will at least show what you remember close to when it happened.

It depends on the exact circumstances. There are circumstances under which a driver would not be at fault, and the conditions that you describe, assuming they are correct, would tend to lead to that conclusion, since if the driver was not at all careless, he would typically not be at fault. However, it's impossible to give you a definitive answer, since at the end of the day, if a legal action is brought, it depends upon what evidence there is of your version of events; what evidence there is of a contrary version; and what a jury (or the judge, if the plaintiff elects a non-jury trial) believes about what the evidence shows. Note that if you are sued, it's up to the plaintiff to make his case, which means that there is an advantage accruing to the defendant (you), in that the burden of proof--of affirmatively proving his case--is on the plaintiff. All that said, a child is, of course, a sympathetic plaintiff, which would help in front of a jury.