Under certain circumstances, yes. All states allow medical exemptions, so children who cannot safely receive certain vaccines are not required to get them. Most states also allow religious exemptions for children whose religion prohibits vaccination. Finally, some states allow philosophic exemptions for people who oppose vaccination on non-religious grounds. To protect themselves and others, unvaccinated students may be prohibited from attending classes if there is an outbreak of a vaccine-preventable disease at their school or in their community.
In Michigan, parents with school-age children have the option to sign a vaccination waiver for philosophical or religious reasons. As of 2015, parents who want a waiver for their child must attend an information session at their local health department.
Michigan Department of Health and Human Services: Vaccine Recommendations and School or Daycare Rules: What is the difference?