Hello.
I was involved in a vehicle-bicycle accident today. I was the driver. The cyclist wasn't hit, just the back tire, so her injuries were minimal. She refused an ambulance and refused to call the police. I helped her out of the road as another witness encouraged her to call EMS. She refused and asked me to just pay for the back tire and be done with it. I agreed, figuring it would just settle the whole thing then and there. She suggested all of this anyway.
Unfortunately, someone called the police. The cyclist told the officer that she did not want to file a police report. The officer then told us that he considered this "civilly resolved" between us and left. He did not take either of our driver licenses, names, or phone numbers, or any other information. I gave her money for a new tire and took her to her house nearby. We exchanged names and phone numbers only, no insurance or driver's licenses.
Later this evening she calls me to tell me that she went to the hospital after I dropped her off and she received some x-rays and would like for me to call her back to discuss it. I did not, I do not feel I owe her anything else.

With no police report and without my information, what recourse does she potentially have?
Would they go so far as to file a report after the fact, use my phone number to find me somehow, and then take further action?
I just worry that she isn't injured at all, because she was legitimately fine when I dropped her off, and I don't want to be taken advantage of.

Thanks for any and all help!

You need to contact your insurance agent now and report this accident to them as this girl will just keep coming back for more money. The next time she contacts you tell her to contact your insurance company and give her the phone number to do so. It was rather foolish on your part not to have a police report filed. Your assssment of her injuries as being minor could be your down fall.

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Unfortunately, someone called the police. The cyclist told the officer that she did not want to file a police report. The officer then told us that he considered this "civilly resolved" between us and left.
...

"Unfortunately"?
On the contrary. The police were called. If the officer chose not to write a report, that's the officer's problem, not yours.


...With no police report and without my information, what recourse does she potentially have?
Would they go so far as to file a report after the fact, use my phone number to find me somehow, and then take further action?
...

She can, of course, sue you and make up all sorts of things. Without a police report, or any other witnesses, it's your word against hers. So, as you have been advised, it's important to contact your insurance company. Let them worry about it.

No, she can't "file a police report". The officer would be the one to do one of those.

She can sue you for everything you have, that is her "option"

You should have asked for the police report, who cares what she wanted, hopefully she is not a con person. But a con person never wants a police report, since that gives them a easier way to sue, since there is no report, they can testify to anything they want.

Next did you get a receipt for the money for the tire ?
I would also worry about the frame being bent also on the bike.

But again, after a few hours, some soreness or pain can develop so this is very believeable.

You need to notify your insurance at once, and give her your insurance info and let them handle it.

Good advice so far. Did you get the name of the officer? If not, I would call the precinct that covers the area and found out who responded to the call. You may need him to testify that the cyclist refused medical treatment.