This is the type of question that should be addressed by a local (Colorado) lawyer because each state has different rules for small claims court and jurisdiction over out of state claims. You may be able to determine for yourself what to do based on Colorado law if you have good reading comprehension skills. In Washington, where I am licensed, I would tell you to sue the person who caused the accident, NOT the insurance company, in small claims court. First of all, your claim is against the at-fault driver, not the insurance company. In Washington, individuals involved in small claims court actions are not allowed to have lawyers represent them in court. That would put you on an equal level with the at-fault driver. Because insurance companies aren't people, they have to be represented by someone in court, usually a lawyer or someone else skilled in presenting cases. You are NOT on the same level as an insurance company representative or lawyer and probably would have no chance in court against a person like that. Check the Colorado statutes and court rules relating to small claims courts. If they are similar to Washington's, sue the individual not the insurance company in small claims court
I'm not licensed in Colorado and am not competent to give you advice about Colorado law. Read the small claims court rules yourself and, if you still have doubts about what to do, pay a Colorado lawyer for half an hour of time to help you..
The prior answer was generally correct. However, I wish to add a few things of which you should be aware. I am not licensed in Colorado, but my comments are applicable to insurance generally.
You may have a cause of action against the at-fault driver and the owner of that vehicle, provided that the driver was using the vehicle with his/her knowledge and consent. If they had liability insurance (rather than collision coverage), the insurer owes both a duty to defend and a duty to indemnify. "Duty to defend" means that the insurer has an obligation to hire a lawyer to defend the other party to try to show that you were either partly at fault, or that not all of the damages that you seek are payable. "Duty to indemnify" refers to the insurers obligation to pay those amounts for which its insured may be determined legally liable.
The other insurer refuses to pay for your damages either because it believes that you were at fault for the collision, or that the amount that you are claiming is unreasonable. Alternatively, it may feel that it has a "coverage defense", meaning that its insured did or failed to do something that it should have done, and for that reason, it does not have to honor the policy. If the latter, there is not a great deal that you can do. If, however, the insurer is not paying because of the liability or damage issues, filing suit is your alternative.
Keep in mind, though, that the insurance company will furnish a lawyer to the person(s) you are suing to defend the claim; you may therefore be out-gunned if you are not experienced in the process. Not knowing the amount involved, I do not know, other than by your statement, whether this will be a small claims case. If it is, it will be generally informal, however, it will still be your burden to prove both liability and damages by a preponderance of the evidence. There may also be a requirement or an option to attend mediation prior to trial. This is a session whereby an independent third person will meet with you, the defendants (and their attorney), together and separately, and try to facilitate a settlement. The mediator does not make decisions as a judge does--he or she tries to make you understand that trials involve risks, that there will be a winner or a loser, but in mediation, you can have more control over the outcome through compromise.
If your damages do not exceed $7500.00, you may sue in mall claims court. The suit is against the other driver, not his insurance company. His insurance company has the obligation to him to provide a defense and to pay any judgment up to policy limits. The insurance company will hire an attorney for him. In that case, you are entitled to have an attorney in small claims court.
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