In Colorado, a title company will do the title search prior to issuing insurance. They research documents which are recorded at the court house; commonly, these are online and can be accessed via an online service.
In response to "aoverbee" below, who stated that they found no reason to purchase title insurance as it only covered items of record; this is incorrect. What would be the point of insurance? There are multiple types of title insurance, and the extended coverage policies may only cost $50 to $100 more than the basic coverage. Never sell a property without paying for title insurance if it is available, and never purchase a property for which the seller does not purchase title insurance if it is available. The cost of the insurance is less than the cost of simply walking into your attorney's door, let alone dealing with a lawsuit. If you have title insurance questions, either a title company or your real estate broker will have good information garding title insurance. If you are not working with a real estate broker, you should consult a real estate attorney to advise you.