I didn't take the breath test. What effect does that have on my arrest?

I am not sure to which "breath test" you are referring. Usually there are two breath tests. One is called the Preliminary Breath Test (PBT) and is administered at the scene. The second is called an Evidential Breath Test (EBT) and is usually taken at the police station. The failure to take the PBT in Michigan is a civil infraction. The failure to take that test is not usually admissible in trial. The general advice is to politely refuse that test.

On the other hand, the failure to take the EBT (in Michigan it is on a DataMaster or DataMaster DMT) can have substantial consequences. The police officer will usually file a notice with the Secretary of State that states that the officer had probable cause to believe you were driving while intoxicated, that the officer arrested you for operating while intoxicated, that he explained to you that you could have an alternative blood, breath or urine test administered by a third party once you took the test being offered by the officer, and that you unreasonably refused. The driver is entitled to a hearing before the Secretary of State state's office. However, that is frequently unsuccessful. The driver's license is suspended for one year unless a circuit court modifies that decision.