Can I claim my vehicle and primary residence both to receive $300 max credit?

Credit for what, exactly?   What "max credit" are you referring to?

The maximum property tax credit of $300

If you're referring to the Connecticut property tax credit, yes, you can claim property tax paid on both your home and vehicle to qualify for the credit.

If this isn't related to the Connecticut property tax credit, can you provide a little bit more background on what credit you are trying to claim so that we can better assist you?