is our responsibility to deduct income tax on salary of previous employer?

We have 30 employees in our Company, some are new joiners in middle of the year. is there our responsibility to deduct IT on salary of their previous employer? for e.g. their previous salary is non taxable but current salary is taxable and end of the year his whole salary is taxable. is there necessary to deduct tax his/her salary of their previous employer too.. please help me out.