Needed to amend 2015 return for a new furnace. does doing so increase audit chances? state return did not change but TT says I need to send that in too?

IRS gets many, many amended returns, so correcting a previously filed return alone does not significantly increase the risk of an audit.  They review each amended return as standard procedure.  I would not worry about the audit risk, I would focus and doing a correct return.

Anytime the Federal return is changed, most states want to see what impact if any it has on the state return, so I would do the amended state return.