KY 3035 follows two-lane Madison Pike north past a pair of elementary schools.

The highway runs atop the city limits of Independence north before leaving the city at Fowler Creek just south of the route's intersection with KY 1486 (Fowler Creek Road) and KY 1829 (Richardson Road), which head east and west, respectively, from the intersection.

KY 3035 crosses Wayman Branch and, at an intersection with an unnumbered Madison Pike, turns northeast fully into the city of Covington to its northern terminus at KY 3716 (Wayman Branch Road).

KY 3035 was originally classified as a supplemental road for its whole length; on October 19, 2004, the agency decreed an upgrade to part of the route's classification to state secondary.

The transportation cabinet transferred the now-unnumbered piece of Madison Pike near KY 3035's northern terminus to county maintenance on May 5, 2011.