Generally not. The Bill of Rights protections that matter most during police encounters are mandated by the U.S. Constitution as interpreted by the U.S. Supreme Court, and all states are required to follow them. States can offer more protection of these rights, but not less.
We frequently hear rumors such as "In Washington State, police can impound your car if you refuse a search," or "In Georgia, refusing a search gives police probable cause." Such claims are absolutely false. Remember that all states must protect your 4th Amendment rights during police encounters.
There are some variations regarding DUI, identification, and parolee searches, but the best strategies for handling a police encounter generally remain the same regardless of which state you're in.
That being said, not all courts are bound by the same rules in the same way. For example, when evidence is obtained unlawfully, that evidence is generally not admissible in court. This is known as the "exclusionary rule" or "fruit of the poisonous tree". There is an exception to this rule where evidence gathered illegally may still be admitted if the police officer believed he was operating within the law. This is called the "good faith" exception, and it is binding in all federal courts and state courts that have adopted the ruling. Some states, however, have not adopted the "good faith" exception. In these courts, it does not apply, and all evidence obtained unlawfully will be excluded regardless of whether or not the police were acting in good faith when they collected it. In many cases, this can mean the difference between having all charges dropped, or going to jail! That's why it's so important to know precisely how the law effects you. If you want to know how your laws work, contact Know My Rights and we'll do a workshop just for you!