Ms. Dammann, 47, could have been defrocked had she been found guilty in the church trial.
The panels look into the validity of the allegations and determine whether further inquiries that might lead to church trials are warranted.
Many priests have been removed from their ministries before a church trial or a full investigation.
Her church trial took place at the Boston meeting house on two consecutive Thursdays in March 1638.
He is also the first priest from the archdiocese in recent memory to undergo a full church trial.
Anne Hutchinson followed in April, after the conclusion of her church trial.
He said he feared that this effort might also be tainted by a church trial.
Church officials said their investigation had uncovered evidence strong enough to warrant a church trial.
This was a church disciplinary trial, not a criminal prosecution, but it was a public sensation.