Sections 52-407aa to 52-407eee, inclusive, govern an agreement to arbitrate made on or after October 1, 2018, except that any proceeding that is governed by chapter 48, 68, 113, 166 or 743b, or any other provision of the general statutes, related to an agreement to arbitrate that was made prior to, on or after October 1, 2018, shall be subject to part II of this chapter, unless:

1. (1)

   1. (A) All the parties to the proceeding agree in a record to be governed by sections 52-407aa to 52-407eee, inclusive, and (B) the agreement under subparagraph (A) of this subdivision is permitted by a law of this state other than sections 52-407aa to 52-407eee, inclusive; or
2. (2) The proceeding is governed by sections 52-407aa to 52-407eee, inclusive, pursuant to a law of this state other than sections 52-407aa to 52-407eee, inclusive.

(P.A. 18-94, S. 3.)