As you take whatever steps that are necessary to avoid probate in Connecticut (which seems to be a passion for many of my clients) you should keep in mind that the probate process for "small" probate estates is pretty quick and straightforward.
"Small" is, of course, a relative term. As far as the State legislature is concerned, your estate is small if your probate assets are under $40,000. "Probate assets" are assets that are solely in the name of the decedent and do not have a designated beneficiary. So, joint assets and things like life insurance policies, annuities, 401K's, IRA's, POD (payable-on-death accounts) etc. are not probate assets.
Please note that the threshold amount for "small" was $20,000, but that was increased to $40,000 in 2007.
Generally speaking, if it's a small estate you only need to file the following with your local probate court (although it may not be long before you won't have a "local" probate court): (1) an "affidavit in lieu of administration" or Form PC-212, (2) original death certificate, (3) the funeral bill and a receipt or outstanding balance amount, if any, and (4) a CT-706NT, which is an estate tax return listing everything that was in the decedent's name so that the Court can confirm that there is no tax.
If there is no will then the remaining funds will be distributed in accordance with the laws of intestacy, which is to say it goes to the next-of-kin under CT law.
If there is a will and the distribution instructions are not consistent with the laws of intestacy then you can still keep it simple if all the heirs waive their right to contest the will. The Court will then simply order distribution pursuant to the will's instructions.
Of course, if the heirs aren't interested in signing waivers for some reason then the will has to be submitted to probate. At that point the simple, expedited process is out the window and you're looking at a full-blown probate process.
If you have some time on your hands and you're not intimidated by judicial forms and some paper-pushing then you can probably tackle a "small" probate process on your own without legal help. Otherwise, it probably makes financial sense to simply hire an experienced probate attorney who can wrap up the process quickly.