In most states an engagement ring is considered a gift and as such you may have no legal recourse to get the ring back. Talk to a matrimonial attorney in your locale to determine what the local courts do wit this kind of action. If you have rights you may have to sue to get the ring back.
When deciding if you should sue someone there are two essential requirements. First, did the person who you think violated your rights have a duty to refrain from the activity that you think would form the basis of a suit or did they have a legal duty to do something and they did not do it. It is very difficult to determine the answer to that question based on the facts you list because it will depend on State law and possibly administrative law in your State and under Federal Law.
The second essential is where there compensable damages? Damages for which a Court can award you monetary awards or injunctive relief (order the other person to do something or stop doing something). If you have both of these elements you may sue.
However, lawsuits take a high degree of expertise and cost money. Many clients have come to me through the years and stated that the money did not matter to them, just the principal of the issue! When I tell them how much I and other lawyers charge by the hour it becomes obvious to them that the value of the lawsuit damages is very important.
You can seek out your lawyer referral service to seek counsel. There are agencies of the State and Federal Government you may want to contact. Talk to a lawyer before you decide to sue someone for expert legal advice!
Disclaimer: This answer does not constitute legal advice. I am admitted in the States of New York, New Jersey and Massachusetts only and make no attempt to opine on matters of law that are not relevant to those three States. This advice is based on general principles of law that may or may not relate to your specific situation. Facts and laws change and these possible changes will affect the advice provided here. Consult an attorney in your locale before you act on any of this advice. You should not rely on this advice alone and nothing in these communications creates an attorney client relationship. The opinions expressed herein are those of the author only and the fact that he has worked as an Assistant District Attorney; State Supreme Court Clerk; Special Assistant United States Attorney (Hawaii); Assistant Cornell University Counsel or Judge Advocate, United States Marine Corps should not be relied upon to assume that these statements reflect the policy of these organizations.
Your question is very general and I am not certain whether all of the material facts have been disclosed. I assume for purposes of your question that both you and your ex-girlfriend reside in Connecticut.
The law in Connecticut regarding your situation is in flux. About 50 years ago, the Court of Common Pleas decided that whether the donee had to return the engagement ring depended on the relative fault of the parties. Thus, if you did not carry through with your promise to marry her, you would be considered at fault and could not recover the ring.
The modern view is that fault should not be a factor in determining who keeps an engagement ring. Rather, the gift of the engagement ring is a conditional gift, the condition being the subsequent marriage of the parties. If the marriage does not take place, the condition has not been met and the ring should be returned to the donor (regardless of fault).
In a recent Superior Court decision, Thorndike v. Demirs, the court adopted the modern no-fault rule and compelled the donee to return the ring. If you file a lawsuit seeking return of the ring, there is authority supportive of your position. Moreover, the majority of states are adopting the modern no-fault rule. I do not know whether you will ultimately prevail, but the law is favorable to your position.