"police are questioning a man who they suspect of strangling his girlfriend to death.. during the interrogation, they ask for a sample of the dirt they can see underneath his fingernails. he refuses and then starts rubbing his fingers on the keys in his pants pocket. may they involuntarily take the scraping? "

They may not take the scrapping involuntary , it won't be accepted as evidence in court

Explanation:

When the case like this happen which has a serious offence and someone is facing a jail sentence a court order will be required from the judge by the police in order for them to get a DNA from the suspect .

The police will need to request a court order which will force the guy to give them his DNA.