Legal Question in Employment Law in Connecticut

If the document is a "covenant not to compete", then generally, this is a legal document. Connecticut and most states allow employers to require employees to sign agreements not to compete against them after their employment ends and for a short (usually one or two years) period of time.

The way you describe the document as one which prevents working with the same skills is different. If it was too broad and was not narrowly drawn to protect the employers' business interests, a court might not enforce it.

You should have a competent employment lawyer review the document.