I purchased a new car this year. How do I include that in my state taxes

You have not mentioned what state you are in.   What are you trying to deduct?  Is the car a personal vehicle or is it used for business?   Did you enter itemized deductions like sales tax when you prepared your federal return?

Itemized deductions are entered in the federal return and flow to the state return.

Federal>Deductions and Credits>Cars and Other Things You Own>Car Registration Fees

https://ttlc.intuit.com/turbotax-support/en-us/help-article/tax-credits-deductions/car-registration-fee-deductible/L0NkGtxYR_US_en_US?uid=ldkhmrss

https://ttlc.intuit.com/turbotax-support/en-us/help-article/tax-credits-deductions/car-registration-fee-deductible/L0NkGtxYR_US_en_US?uid=ltrwny3c

SALES TAX

You can enter the sales tax you paid for the car you purchased in 2023 by going to Federal>Deductions and Credits>Estimates and Other Taxes Paid> Sales Tax.  You will be asked if you paid sales tax on a major purchase, and you will be able to enter the sales tax you paid for your new vehicle. 

Sales tax is an itemized deduction.  Unless you have enough other itemized deductions to exceed your standard deduction the sales tax will have no effect on your tax due or refund.

“Major purchases” that you can enter for the sales tax deduction include:

Motor Vehicles (cars, trucks, motor homes, RV’s, sport utility vehicles and off-road vehicles

Aircraft or boats

Mobile homes

Manufactured housing

Building materials for major home improvements

You cannot deduct: furniture, jewelry, home electronics such as TV’s or computers

https://ttlc.intuit.com/questions/1901222-which-deduction-should-i-choose-sales-tax-or-income-tax

https://ttlc.intuit.com/questions/2566624-how-much-sales-tax-did-i-pay-last-year

https://ttlc.intuit.com/questions/3148443-how-do-you-define-major-purchase-or-major-item-for-the-sales-tax-deduction

https://ttlc.intuit.com/questions/1900791-how-do-i-find-my-local-sales-tax

https://ttlc.intuit.com/questions/2566624-how-much-sales-tax-did-i-pay-last-year

States with no sales tax:  Alaska, Delaware, Montana, New Hampshire and Oregon

Unless you are self-employed or a business owner, there is no deduction for the purchase of a new car.