First, I am ethically obligated to advise you that I do not practice in Wyoming, and I am not licensed to practice in Wyoming.
In light of the recent United States Supreme Court case of Arizona v. Gant, you may be able to argue the search was unreasonable as it was unnecessary for officer safety. http://en.wikipedia.org/wiki/Arizona_v._Gant. On the other hand, this case may not apply to you, as you were likely arrested before it was decided.
I strongly urge you to consult with an attorney, if you have not done so already. Most initial consults are free. So, you have nothing to lose. I can recommend the following member of the National College of DUI Defense in your state:
R. Michael Vang, Sustaining Member; State Delegate
119 Grand Avenue
Laramie, WY 82073
Under the recent United States Supreme Court case of Arizona v. Gant, (___ U.S. ____ 2009) police officers cannot search the vehicle if you had not been inside when arrested. So, Gant may not protect you in this situation. Gant does not apply, however, when the police are reasonably searching for evidence of a crime. If you were arrested for giving false information, the police may have been legitimately searching for evidence, depending on the circumstances.
The Fourth Amendment of the Constitution, as it is generally understood, protects you from unreasonable search and seizure. Check my Legal Guide " Constitutional Law: Can the Police Search My Car?"
In your situation, you might have an argument to supress the items uncovered in the search of the car.
Each situation is very fact specific. You may want to consult a skilled criminal defense lawyer in your locale.
You might find my Legal Guide helpful "How to Choose A Lawyer For You"
You might find my Legal Guide helpful " What Do I Tell My Lawyer"
Good luck to you.
God bless. I am in Chicago and do not practice in your state.
NOTE: This answer is made available by the out-of-state lawyer for educational purposes only. By using or participating in this site you understand that there is no attorney client privilege between you and the attorney responding. This site should not be used as a substitute for competent legal advice from a licensed professional attorney that practices in your state in the subject practice discipline and with whom you have an atttorney client relationship along with all the privileges that relationship provides. The law changes frequently and varies from jurisdiction to jurisdiction. The information and materials provided are general in nature, and may not apply to a specific factual or legal circumstance described in the question.