Cohoe was assigned the case after six other judges recused themselves.
He declined to comment Monday about his assignment to the Brame case. Judges often refuse to talk publicly about cases before hearing them.
Brame's family has sued the City of Tacoma, claiming it covered up wrongdoing by Police Chief David Brame, who fatally shot his wife and himself April 26.
Cohoe ascended to the Superior Court bench in 1987 after working as a private attorney.
He has heard numerous civil and criminal cases and has presided over the county's drug court, where certain people convicted of drug crimes can get a shot at treatment instead of incarceration.
In November, advocates for domestic violence victims criticized one of his rulings in a 2002 divorce case. Cohoe ruled that a woman who had obtained a permanent domestic violence protection order against her husband - former King County sheriff's deputy Dawud Muhammad - was not entitled to half the pension benefits he had accrued during their marriage.
Cohoe told Cherry Gilbert she should have known she was destroying her then-husband's career by obtaining the protection order. The order forbid Muhammad from owning or possessing a firearm, which essentially ended his career.
In obtaining the protection order, Gilbert had accused Muhammad of threatening her with a gun during an argument.
In November, a state appellate court upheld Cohoe's ruling on a 2-1 vote.
At least one women's group complained the ruling would unfairly force other domestic violence victims to choose between their personal safety or their financial well-being.
On Monday, Tim Gosselin, who is representing the City of Tacoma in the Crystal Brame case, called Cohoe "a fine and respected member of the Pierce County bench."
Gosselin said judges make unpopular decisions as a part of their jobs, and that Cohoe's ruling in the Gilbert case should not necessarily affect his ability to fairly hear the Crystal Brame lawsuit.
Paul Luvera, who is representing Crystal Brame's family, said he will review Cohoe's record and take "appropriate legal procedures" if he decides the judge should not hear the case.
"They'll be doing their homework tonight," said Mark Firmani, a spokesman for Luvera.