I'm a single male in my mid-20s that has been renting an apartment in
a high-tax area in CT for the past year. I feel as though I may have
made a mistake in changing my "permanent" address with my car
insurance company and the Dept. of Motor Vehicles to the new address,
rather than keeping it at my mother's house (within CT) where I lived
prior to moving last year.

Since changing the address, I am paying considerably higher property
tax for my vehicle and my car insurance more than doubled.

Since I do not own my house, can I get away with reverting to using my
mother's address as my permanent address? Could I run into trouble if
I get into a car accident?

from a insurance manual:
The premium for an automobile shall be determined on the basis of the
United States Postal Services ZIP Code applicable where the automobile
is principally garaged.