I later realized I should have left a note, so I called back to the business where the incident occurred (small parking lot) and asked if anyone came in regarding the incident (which no one had) and I explained to them what happened and left my name and phone number. I am now wondering if I need to contact the police department to notify them of the incident, or do I just wait and see what happens?
Technically this is a hit and run. However, it sounds like there was little or no damage and you did make a reasonable effort (albeit after the fact) to leave your contact information in case someone were to go into the store and seek information. Although this is a reasonable attempt to leave your contact information, as you stated, you should have left a note on the car you hit as soon as you realized there might be damage. I would not report this to the police, but if the driver does report it to the police before he is able to contact you, and the police investigate (which is unlikely given the nature of the incident) you could certainly be charged. If charged and you made good on the damage, there is a good chance any charged could get dismissed. This is a long answer for a short question, but I would wait and see what happens.
The information provided is general in nature based on the limited information provided and does not constitute an attorney client relationship. This attorney is licensed only in the State of Washington and is not rendering you legal advice. The information given is for educational purposes only. The best advice would be to consult with an attorney in your local jurisdiction for answers and opinions based on specific and more detailed information relevant to your case specific question and the relevant laws in your area.