If someone committed a crime and got arrested with my vehicle, can I be charged with what they did?

What I think that you are afraid of is being charged as an accessory to the crime or what is known as aiding and abetting in some jurisdictions.  You would have to check the statutes in your state becuase under different state laws, aiding and abetting and accessory vary greatly regarding their definition. Depending on the action of the crime, the participation could elevate to a conspiracy crime.  Under most legal jurisdictions, the person or persons charged with aiding and abetting or accessory are not directly involved with the crime that is committed. They are usually not present when the crime occurred. I would speak with an attorney in your area.  Good luck.

Being guilty of a crime depends on mental state or intention. If someone did not know that a vehicle was going to be used in a crime--which includes not having reason to know of it; i.e. you can't willfully turn a blind eye if the warning signs were there--and did not otherwise intend or authorize the vehicle to be used in a crime, then that person should not be criminal liable. That's the law; as a practical matter, the authorities may not believe you. They would have to prove that you knew or intended the vehicle to be used in a crime to get a conviction, but the threshold for initially arresting someone is much lower than the threshold for conviction, so if the authorities have reason to believe you facilitated the crimes, they may choose to take action--just that at some point, they'd have to be able to prove that, and you'd also have the chance to present defenses.