The difficulties here are that when you take a plea, you give up the right to challenge the evidence against you at hearings and trial. Further, even under the best of circumstances, it is very difficult to take a plea back once a defendant has committed on the record to it and been sentenced. That's because a judge won't sign off on a plea unless he's sure that a defendant is taking it voluntarily and of his own free will, knowing that he's waiving his rights to challenge the evidence against him at hearings and trial and after having been counseled by an attorney. He would also have stated on the record that he pled guilty because he actually was guilty.
To that effect there is always some kind of a plea allocution -- statements put on the record or signed off on by the defendant -- the purpose of which is to make the plea airtight. Your words were taken down by a court reporter and can be used against you at any hearing to reopen your case and vacate your conviction.
There are some exceptions to the general, rule of course. Typically, they involve Constitutional issues, such as lack of jurisdiction, a denial of due process, newly discovered exculpatory evidence, or an unlawful sentence.
Finally, you have waited 16 years to address this.
However, if what you want is an expungement, you do not need to reopen your old case. You would already be eligible to apply to the governor for an absolute pardon. If it were granted, that would completely erase your Connecticut criminal record. You can see the information about the pardon here. It will link you to the forms you'd need to download to get this done.