Yes, a CT Will must be notarized and witnessed by individuals not named in the Will and unrelated to the person for whom the Will is created. The Norary may be the Attorney who prepared it as a "commissioner of the court" or a separate Notary appointed by the State of CT.
No. There is no statutory requirement that a Connecticut will be notarized. The statutory requirements are that the will be signed at the end of the document in front of two witnesses who sign it in the testator's presence [Sec. 45-251, CT General Statutes]
That being said, it is common practice in CT to use a "self proving affidavit". This is a statement by the witnesses under oath in front of a notary or a lawyer [Commissioner of the Superior Court] that the testator had the requisite capacity to execute a will.
A will will not fail because it is not notarized. The Probate Court may ask for an affidavit from the witnesses or that they appear in court. If a will is contested, the testimony of only one witness will be sufficient to establish prima facie evidence of capacity. [Wheat v. Wheat]