Instead, a set of stipulated facts negotiated by both sides will be presented Thursday afternoon to Judge John M. Torrence.
Mike Mansur, a spokesman for Jackson County prosecutor Jean Peters Baker, said a verdict is expected by the end of the day.
The charges stem from the Rev. Shawn Ratigan's child porn case, in which church officials knew about photos on the priest's computer but didn't turn him in for six months.
Finn has argued that he was not the diocese's mandated reporter under the law at the time, the responsibility rested mainly with Vicar General Robert Murphy so Finn should not face charges. Attorneys for both Finn and the diocese also have argued that the state's law is unconstitutional.
Mansur said the decision to have a judge, instead of a jury, hear the case so close to the scheduled jury trial is unusual but not unprecedented.
"Bench trials are not typical, but they do happen," Mansur said. "Nothing about this case has been particularly typical."
A computer technician found child pornography on Ratigan's laptop in December 2010, and reported it to the diocese. Of the hundreds of images found, many focused on the crotch areas of clothed children and one series showed the exposed genitals of a girl believed to be 3 or 4 years old.
Finn has acknowledged he was told in December 2010 about the images. The bishop also has acknowledged that a parochial school principal had raised concerns about Ratigan's behavior around children in May 2010, half a year before the photos were found.
State law requires that the Division of Family Services be informed of such evidence of abuse.
Murphy confronted Ratigan about the photos, and the next day, Ratigan was found in his garage with his motorcycle running and a suicide note that apologized for any harm he had caused. Ratigan recovered after being hospitalized.
Finn sent Ratigan out of state for a psychological examination, and then ordered him to stay at a convent in Independence, Mo., where he could say Mass for the nuns. Finn also ordered Ratigan to avoid contact with children.
Later, after the diocese received reports Ratigan had attended a St. Patrick's Day parade and a child's birthday party, Finn ordered that police be given copies of the photos recovered from Ratigan's laptop.
Ratigan pleaded guilty last month to federal charges of producing and attempting to produce child pornography, admitting to taking photos of children 2 to 9 years old. Prosecutors said they will request that he spend the rest of his life in prison. A sentencing date has not been set.