How can I get my arrestand fingerprint record removed from public record after dismissal upon completion of my probation?

What you want to d is to have your arrest record "expunged" from the system.  State law varies on the type of offenses permitted to be expunged and expungement itself.  New York, for example, only seals records and does not expunge - or delete - them.  Michigan has what is known as a statute that allows records to be "set aside" rather than deleted.  They can still be accessed by some groups.  The records cannot be accessed for general law enforcement or civil use. An set-aside record may be considered in employment applications for law enforcement positions and licensing. Expunged records of may still be used as a prior conviction when applicable in subsequent sentencing. M.C.L. § 780.623. Setting aside of an offense doesn’t relieve anyone of a duty to register as a sex offender. M.C.L. § 780.622. Juvenile records of diverted sentences are to be destroyed within 28 days after they turn 17. M.C.L. § 722.828.

Eligible records are records of first convictions under M.C.L. § 780.621.  Generally arrests that result in dismissals also qualify but check on how that is done through counsel in your area. You need to file paperwork with the court and go before a judge.  The clerk of the criminal court may also be able to help. Good luck.