Yes, Connecticut does permit the auto owner the option of self insuring.

Subject to approval of the Insurance Commissioner the security required by this section, may be provided by self-insurance by filing with the commissioner in satisfactory form: (1) A continuing undertaking by the owner or other appropriate person to perform all obligations imposed by this section; (2) evidence that appropriate provision exists for the prompt and efficient administration of all claims, benefits, and obligations provided by this section; and (3) evidence that reliable financial arrangements, deposits or commitments exist providing assurance for payment of all obligations imposed by this section substantially equivalent to those afforded by a policy of insurance that would comply with this section. A person who provides security under this subsection is a self-insurer. A municipality may provide the security required under this section by filing with the commissioner a notice that it is a self-insurer. C.G. S. Section 38a-371(c).

However, it is still regarded as a form of insurance regulated by the State Insurance Commissioner, and subject to the same liabilities in claims administration. Either way the auto owner is required by law to have it. He is going to pay out either a premium for a policy or pay out sufficient security satisfactory to the State. I fail to see the distinction you are making.