The highway has its western terminus at SR 123 approximately 2.50 miles (4.02 km) southeast of Lebanon, and just southeast of the interchange Interstate 71 (I-71) has with SR 123 at its exit 32.

SR 350 passes through portions of Warren and Clinton Counties along its way.

The NHS is a network of highways determined to be most important for the nation's economy, mobility and defense.

The highway originally ran entirely within Warren County, along its current alignment from its western terminus at SR 123 southeast of Lebanon to its junction with the concurrency of U.S. Route 22 (US 22) and SR 3 west of Clarksville.

[6][7] One year later, SR 350 was extended via a short concurrency southeast with SR 73, then northeasterly along a new state highway alignment to Sabina, where it intersected US 22/SR 3 a second time, and came to an end.