if i do not apear for an ohio misdameanor court date will a warrant travel to ny

i was arrested friday for criminal mischief in in ohio on my way from buffalo where i live. when me and two friends stopped at the ohio welcome center we wrote with washable marker on the walls of the stall nothing excessive just our nick name D.N.A and saying GET NOODLED we were arrested 20 miles down the interstate cuffed read our rights than brought to jail where they took our money for "booking fee's" than released with a summons to be back in ohio on tuesday if we do not show up to court cause we have no way of getting there what will happen if we just never go back to ohio and dont go to court?