Route 341 begins as a continuation of County [Route 3 (Dutchess County, New York)|Dutchess County Route 3] at the New York state line in Kent and heads southeast along BogHollow Brook and Macedonia Brook. It crosses the Housatonic River and continues southeast, then turns east and northeast across the town into Warren. In Warren, it continues generally east to the center of town, then turns south for a long overlap with Route 45. After leaving Route 45, it turns southeast to the southeast corner of Warren and crosses into Washington. In Washington, it turns south to end at an intersection with U.S. [Route 202 in Connecticut|U.S. Route 202] by the Shepaug River in the Woodville section of town.