I paid my vehicle registration in 2018, the smog check wasn't completed until 2019. The CA DMV doesn't show it as processed until 2019. To which tax year does it apply?

TurboTaxMichaelL1 I think nailed it. I used the CA DMV on-line "Vehicle License Fee" calculator. The total registration amount was ~$325.00, however the Vehicle License Fee portion is only $27.00. So the $27 is what I will use on my taxes.

If the tax was paid in 2018, and it was owed in 2018, then it is deductible in 2018, regardless of how long it took the state to process the payment.

EDITED 1-15-2019 2:52 PM (CST) to add section below:

The vehicle registration is deductible only if it is a tax.  It has to be based on the value on the vehicle. Some states only part of it is deductible as some have a flat fee plus part is based on the value.

See below for more detail on your respective state.

https://ttlc.intuit.com/replies/6145391

is vehicle registration even a tax? 

In many states the "registration" fee itself is NOT deductible.   Only that portion of the fee that is a property tax  based on the vehicles value is deductible.   Not all states have a vehicle property tax.   Most states that do will list it separately on the registration bill.

In California, for example, the following is a list of the various fees that may be included in your annual vehicle registration payment:

   - Registration Fee
    -Vehicle License Fee (This is the fee that may be an income tax deduction)
    -Weight Fee
    -Special Plate Fee
    -County/District Fees
    -Owner Responsibility Fee