Conn. Gen. Stat. § 14-233: Passing on right.

The driver of a vehicle may overtake and pass upon the right of another vehicle only when conditions permit such movement in safety and under the following conditions: (1) When the vehicle overtaken is making or has signified the intention to make a left turn; (2) when lines of vehicles traveling in the same direction in adjoining traffic lanes have come to a stop or have reduced their speed; (3) upon a one-way street free from obstructions and of sufficient width for two or more lines of moving vehicles; (4) upon a limited access highway or parkway free from obstructions with three or more lanes provided for traffic in one direction. Such movement shall not be made by driving off the pavement or main-traveled portion of the highway except where lane designations, signs, signals or markings provide for such movement. Violation of any provision of this section shall be an infraction.