Who polices Durham
Durham has no municipal police department. The town is covered by a resident state trooper assigned from Connecticut State Police Troop F, based in Westbrook, so an arrest in Durham is a state police arrest.
A resident trooper is assigned to the town rather than passing through it. The practical points for a reader are that booking runs through the state police and that the number to call about someone being held is the troop, not a local station.
Route 17 runs through the town and carries much of the traffic enforcement.
Where your case goes
Durham cases are prosecuted at Middletown Superior Court, GA 9, the next town north. The court page covers parking and the morning docket.
If troopers released you, your date is on the paperwork they gave you. If you were held, court is the next business day, where a judge reviews the bond.
After the arrest
Troopers either release you from the barracks on a promise to appear or after a bond, or hold you for court the next business day. Released, your date is on the paperwork you were given. The arrest page covers booking and the bond and bail page covers the bond.
The most useful thing you can do before the date costs nothing: stop talking about what happened. People talk themselves into worse charges at this stage than at any other.
A family violence arrest goes to court the next business day either way, with a protective order issued at that appearance. The arraignment page covers what that date involves and the what to expect page covers the rest.
Common charges in Durham
Route 17 traffic work puts DUI and drug possession among the more common Durham charges at GA 9. Assault, domestic violence and family violence, and larceny and shoplifting account for the rest of a small docket. For someone with no record the question is usually which diversionary program fits.