I am  a lawyer in CT and practice in this area of the law.  If you are planning on driving the car on public roads then you must get the car registered.  If the car is completely totaled and you do not plan on driving it, but rather collecting the insurance money and getting a new car, you do not need to register the car.  I suggest seeking damages from the other driver for your car to avoid using your insurance. 

I am a CA lawyer.  I agree with the response from CT lawyer.  There is an ironic aspect to this.  If you registered your car, you would be entitled to be reimbursed for the unused portion.   So with your car being a total loss, you will not get reimbursed because you did not make the registration payment.  One additional thought:  keep the car off of the street or you will get a ticket for having an expired registration.  good luck.