With the caveat that I am NOT offering legal advice as an attorney, just my take on the GENERAL rules and regulations, and that you should consult an attorney or knowledgeable LEO in your state before doing something you think might be illegal:
In general, it is legal for a citizen to wear a ballistic vest in every state of the Union. However, CT, and possibly other states as well, restricts the sale of such armor to face-to-face sales unless the purchaser is an LEO. Moreover, many state legal codes prohibit felons from wearing armor, and in other states, probation and parole requirements accomplish much the same ban. Also, as has been mentioned in this thread already, wearing armor in the commission of a felony (sometimes an A or B misdemeanor) is also a crime. This means basically, that you’re going to get hit with some extra prison time for the armor if convicted of the primary crime.
I personally have worn a concealed vest on a regular basis in several states, including IL, without any legal problems, but you may get the evil eye from an LEO now and then.
Please do not rely on the above as legal advice. I am not your attorney, you are not paying me to advise you, I only practice in Indiana, and we have no attorney-client confidential relationship.