If you are hurt, then the short answer is yes. Like all insurance claims, if the insurance company doesn’t know you were hurt then they can’t help you. Relying on your employer to file for you shows a level of optimism that I recommend against.
The act of filing is pretty straightforward, if you are injured you must send a Form 30C to the Workers’ Compensation Commissioner for the district you were injured and to your employer. If you are a State of Connecticut employee you must also send the 30C to the Commissioner of Administrative Services, 165 Capitol Avenue Hartford, CT 06106. An original signature version should go to the employer. You must deliver the form either personally (and if so get a receipt) or through registered/certified mail.
The form has four sections, the first is to identify the injured worker, the second to identify the employer, the third to describe the injury, and the fourth is for signature.
The third box, Injury, is the trickiest one. Describing the injury too narrowly can cause difficulties down the road, for instance you suffered what you believe to be a meniscus tear in your knee, and your draft the 30C as such. Closer examination reveals a torn anterior crucial ligament. The mistake on the 30C will not likely be fatal, but it can complicate matters a great deal. It is sufficient to indicate that you hurt you (left or right) knee. So, remember the simpler the better.
Generally, when a person is injured at work it is from a single traumatic event, e.g. they fell down some stairs – making describing how the injury occurred relatively easy, but sometimes an injury is considered an occupational disease or the result of a repetitive motion. If this more accurately describes your injury than box describing the injury as such MUST be checked.
Finally, the Injury box also contains areas to check if you worked more than one job at the time of the injury. This is referred to as concurrent employment and you must alert the Commissioner’s office if you had more than one employer. There are implications for your employer’s insurance if you held more than one job at the time of the injury.