if mother as sole custody and I'm already paying child support who's responsible for health insurance

The cost of health insurnace is an expense over and above basic child support. The court is obligated to make sure the children are insured. One or both of you can be court ordered to provide the health insurance plan. The costs can be divided equally by both parties or set on a pro rata basis based on the percentage of time you both spend with the children. It can also be a factor under DCF guidelines as an offset on the amount of support paid.

I recently wrote a blog on this very topic, at our law firm's site web site. The answer to your question is yes: where you  have minor children, the court is required to order the parties to share in the  cost of health insurance and uninsured medical costs, regardless of the other financial obligations of supporting the children.