In Florida you can. Where you go depends upon which court issued the no-contact order (eg Dependancy Court, Domestic Violence Court, Family Court) .
You probably have to file your pleading in that Court and appear before the judge. Or you might have to file an appeal before a higher (appeal) court. You must speak to a Connecticut attorney that practices in this field of law.
The answer depends on a number of factors. It cannot be answered in a vacuum on an online service. You should arrange for a consult with an attorney who specializes in these kinds of issues.