Yes, the matter is serious. If this case happened in Washington, your friend could be charged with Hit and Run Unattended, RCW 46.52.010. The charge is a simple misdemeanor criminal offense punishable by up to a maximum of 90 days in jail and a $1,000.00 fine.
Washington law requires that if you collide with a parked or otherwise unattended vehicle you must immediately stop and locate and notify the operator or owner of the vehicle and provide them with your name and address. If you cannot locate the owner or operator, you must leave a written notice with your name and address in a conspicuous place. Failure to do this constitutes the crime of Hit and Run Unattended.
Fortunately, there are many potential ways to resolve these cases and avoid a criminal conviction. While Hit and Run Unattended is a crime, many prosecutors (the people who bring the criminal charges against you) and courts are willing allow these cases to be resolved without a plea of guilty.
Some possible ways to resolve your case include things like a "compromise of misdemeanor" a "diversion" or "continuance with a dismissal" or a "bail forfeiture" which may allow you to avoid a criminal conviction and keep your record "clean." Unfortunately, not all courts allow such programs and not all prosecutors are willing to resolve cases this way.
Although a conviction for hit and run unattended will not suspend or revoke your friend's driver's license, it may increase their insurance costs. This is a small price to pay, however. Perhaps if your friend contact authorities immediately, their investigation would have showed the victim's car was parked illegally.
I agree with my colleague, that these matters are viewed seriously by the State of CT. I suggest your friend review the law at http://www.deadlyroads.com/laws/connecticut-hit-and-run-laws.shtml and then discuss this with an experienced criminal defense lawyer admitted to practice law in CT.
As to whether their insurance will cover an unreported accident is determined by the explicit terms of the insurance policy, which typically requires that the accident be reported within a certain set period of time. Your friend should review the terms of the policy and then discuss this with the lawyer as well. Good luck.
Disclaimer: The above answer does not constitute legal advice, attorney advertising, or establish an attorney-client privilege; and, is offered for the limited purpose of educating the requester as to the potential legal issues they need to discuss with a lawyer in their State. I strongly recommend you discuss this situation with an experienced criminal defense lawyer admitted to practice law in your State before you make any decisions as to how to proceed. Do not presume that any legal analysis that may apply in NJ where I practice would apply in your State or under the facts and circumstances of your case, unless an attorney admitted in your State advises you that it applies to you and your case.