The answer is maybe. You have to meet the requirements of the MVD. If your license was suspended for refusing a chemical/blood test you have the option of applying to MVD for what is known as a SPECIAL IGNITION INTERLOCK RESTRICTED DRIVERS LICENSE (SIIRDL).
“After completing not less than ninety consecutive days of the period of suspension required by this section and any alcohol or other drug screening that is ordered by the department pursuant to this chapter, a person whose driving privilege is suspended pursuant to this section may apply to the department for a special ignition interlock restricted driver license pursuant to section 28-1401. Unless the certified ignition interlock period is extended by the department pursuant to section 28-1461, a person who is issued a special ignition interlock restricted driver license as provided in this subsection shall maintain a functioning certified ignition interlock device in compliance with this chapter during the remaining period of the suspension prescribed by this section. This subsection does not apply to a person whose driving privilege is suspended for a second or subsequent refusal within a period of eighty-four months.”