It depends. You only need to have IN withhold tax, state and local will be taken. When you file your IL resident return, they will give you credit for the state tax paid to IN. IN does have a reciprocal agreement with many states to not withhold taxes. However, IN is not one of them. See Nonresident Employees of IN. You will need to file a nonresident IN and resident IL return while working in IN.
Since IL has a higher state tax than IN, you would either want to have extra taxes withheld for the difference or you could make estimated payments to IL.
When you are in a situation where you live in one state and work in another state without a reciprocal agreement between the states, you file two state returns. FIRST you prepare a return for the NON-resident state, and then you prepare a return for the state you live in.