Forty-one-year-old Levon Warner and 35-year-old Eric Floyd could face the death penalty in the May 2008 shooting death of Sgt. Stephen Liczbinski.
The prosecution and the defense are expected to make their closing arguments Thursday.
Then, a jury must decide whether to sentence Floyd and Warner to death - or give them life in prison.
The men were convicted last month of first-degree murder in Liczbinski's killing, although neither pulled the trigger.
Authorities say the gunman, 33-year-old Howard Cain, was killed in a shootout with police.