You could lump your local school taxes paid in with your property taxes paid, yes. But it would be more proper to break it out separately as "other taxes paid," or, if the school tax is based on income, rather than the value of your property, you could include it along with your state income taxes paid (if any).
Basically, it all comes out the same in the wash, so to speak, no matter how you enter it into TurboTax. What the program will do for your school taxes is add it to your other amounts, if any, on your Form 1040 Schedule A (itemized deductions). No matter on which line your school taxes paid eventually lands, the column on numbers, when added up together, should total the same thing.
Because this is easier to visualize with an image, than to explain in words, please see the screen-capture attachment to this answer, and it should all make better sense.