The 2016 Democratic Party Platform, which was released on July 21, says that Democrats "will strengthen the [nuclear Nonproliferation Treaty], push for the ratification of the Comprehensive Nuclear-Test-Ban Treaty, and stop the spread of loose nuclear material."
This is modified slightly from the 2012 party platform which declares: "We will also work to ratify the Comprehensive Test Ban Treaty and seek a new Fissile Material Cut-off Treaty that prohibits the production of fissile materials intended for use in nuclear weapons."
While the 2016 Republican Party Platform does not specifically mention the CTBT, it states: "We should abandon arms control treaties that benefit our adversaries without improving our national security."