You cannot refuse to give a blood sample in a NJ DUI. As with giving breath samples for a Breathalyzer, New Jersey law requires you to give a blood sample, where appropriate, to determine your Blood Alcohol Content (BAC). Blood samples, however, can be taken involuntarily, as long as the police use "reasonable force" to do so.
A blood draw is considered a "search and seizure" under the Fourth Amendment, and as such must be done pursuant to probable cause. Therefore the police must meet this burden, otherwise the BAC reading can be thrown out by the court. It can also be thrown out if it was obtained through an "unreasonable use of force."
Blood samples are usually requested when you were injured in an accident that gave rise to the arrest or when you refuse to give a breath sample. Charges can also be based on blood tests done by the hospital as part of the treatment for your injuries.