I'm sorry to hear about your aggravation, but if your positions were reversed, I would have told you to make a police report as well. There are a number of important reasons, the most important being to document the incident for an application for benefits as well as pursuing the mini-tort under Michigan law. Anyways, you haven't given any information on how the car accident occurred so it is hard to advise you on whether and how to dispute it. I can only assume from a ticket for failure to stop, which is probably a failure to yield within the assured clear distance that you probably rear-ended the woman in front of you. If you have an overall pretty good record it is probably worth your time to go to court, in which case the ticket could be dismissed entirely if the police office does not show, or if you show you are an excellent driver, with no prior accidents and only one speeding ticket, and that this was an extremely minor no injury accident (this is very important by the way) the ticket might be pled as a non-moving violation, which means you pay the fine but there are no points added to your record and no increase in your insurance rates. Good luck.
In some states you can plea nolo contendere, pay a fine & the charge will not appear on your record. Check /w a local traffic attorney in your area.