I'm not sure of your financial situation, but the moment she signs on the dotted line, you are on the hook for half the vehicle. I believe the lease would be considered a martial debt, depending on the state you live in.
Me: 43 W: 37 Together: 18 M: 15 D: 8 yrs old ILYBNILWY: March 2011 She Filed for D: August 2011 She moved out: Sept 1, 2011 Reconciled: May 2012 Divorce Case dropped: July 2012