If your vehicle is safe to drive, the insurance company of the owner at fault will either ask you to take your car to a reputable repair shop, or will arrange for an “appraiser” to see your car, evaluate the damage, and make an estimate of repair costs.
No matter who makes the estimate, the expected repair costs are only an estimate at this point. If more damage from the collision is found while repairs are being made, the shop and insurance company will reach an agreement about the extra work to be done and how much will be paid to do it.
Some insurance company’s have repair shops to recommend-and some insurance company representatives really push you to use the “approved” shop. In Connecticut, the choice of where the repair is done is yours.