The above answers assume you are a regular W-2 employee.  The answer will be different if you are a contract employee/independent contractor receiving a 1099-Misc or 1099-NEC. 

Be advised that Ohio does a convoluted tax calculation for non-residents/part year residents. It calculates tax on total income, then it calculates a non resident/part year resident credit, which it subtracts from the tax it calculated on the total income. The credit is calculated as your non-Ohio income divided by Total adjusted Income multiplied by the total tax. TurboTax (TT)   does this by allocating your income as either Ohio or non-Ohio. W-2 income will be allocated by the state name abbreviation shown in box 15 of your W-2. TT will ask you, item by item, in the state section, how much of your other income is Ohio or non-Ohio income.

Be advised that you will probably have to use a work around to get TT to prepare the OH return correctly. At the w-2 screen split the boxes 15-20 W-2 info into 2 lines. On the 1st line put OH in box 15 and the portion of the CA income since Feb in  box 16. Leave box 17 blank.  On the 2nd line put CA in box 15 and the  wages  before the move  in box 16; leave the CA withholding in box 17.