I moved from California to Kentucky. My employer paid for my move and grossed-up the amount so I don't have to pay the taxes. Do I need to report it when I file my taxes?

No, you do not need to report your reimbursement separately since it is included as part of your wages. However, you may get a deduction on both your state returns for any moving costs you paid. Any costs paid directly by your employer would not be deductible, but the costs that you paid would be deductible since they are reported on your W-2. To report these:

1. Go to Federal > Deductions & Credits > Other Deductions and Credits > Moving Expenses.
2. Click Add a Move and enter the required information. 
3. Make sure you only enter expenses that were paid by you even though your employer reimbursed you. Do not enter the movers' expenses since that was paid directly by your employer.

The moving expense deduction has been temporarily suspended due to the Tax Cuts and Jobs Act of 2017, unless the move is due to military orders.