Leaving the scene - insurance wants me to pay up

Hello from Minnesota
I hit another car that was stopped on an on ramp at about 20 miles an hour.
I left the scene of the accident and drove home. (Yes I know this was not the right thing to do). The police came to my door and saw me but I did not answer the door. A month went by with no notice, but yesterday I received a letter from State Farm stating I was responsible for the damages to there insurer and they were preparing the bill for me to pay. There was a police report with the letter stating that the other party saw my license plate, but did not see who was driving. In the accident report the police stated they saw a 6foot man with brown hair(me) through the front window who did not respond when they showed up to my residence, they also noted they saw a 4 door blue sedan with damage to the front end through the window of my garage which matched the other party's description of the car and the damage corresponded to the damage to the other partys vehicle left rear. (I actually have a 2 door blue compact).

Questions -

1. If I don’t pay the claim to State Farm will they sue me?
2. If I do pay can the police charge me with the crime? (Since they have not yet).
3. What kind of charges can the police charge me with?
4. Why haven’t the police charged me yet? They seem to have plenty of evidence (I guess they don’t know who was driving the car, so they don’t know who to charge with leaving the scene).

Thanks much for your response.