can i refuse a lie detector test

You should not take a lie detector test, especially without an attorney present.  It works like this:  The police need probable cause to arrest you for any crime.  Moreover, polygraph tests are not conclusive.  Therefore, if the police already have probable cause to arrest you prior to taking the polygraph test, they will do so regardless of your success or failure with respect to the test.  Thus, if the police have probable cause to arrest you and you pass the test, that will not negate probable cause -- the police may just interpret it as a false negative.  However, if the police do not have probable cause to arrest you but then you fail the test, the failed test result MAY give the police probable cause to arrest you.  What this means, in practical terms, is that taking a polygraph test will do very little to exonerate you, but can potentially be used to incriminate you, even with a false positive.  However, since these are serious accusations I suggest that you consult with and/or retain a skilled criminal defense attorney prior to making any further decisions (or having any more conversations with the police) with respect to this matter.  After discussing the specific facts of this matter with a criminal defense attorney, he or she will be able to more specifically advise you with respect to the best course of action in this particular instance.  Thus, in some limited situations a criminal defense attorney may, in fact suggest taking a polygraph test under certain circumstances.  Regardless, you should consult with and/or retain a criminal defense attorney at your earliest convenience.