No, don't add them together.
Ad Valorem taxes are entered under Property Taxes (Deductions & Credits >> Your Home). In TurboTax desktop, search on "property taxes - real estate" and use the "jump to..." link to go to that section. See screenshot below - click to enlarge.
Personal Property Taxes (non-ad valorem) are entered separately under Deductions & Credits >> Cars and Other Things You Own. Search on "personal property taxes" and use the "jump to..." link for this section.