Two workers from the Good Shepherd shelter on Toronto's Queen Street East testified at Kachkar's trial on Tuesday.
Kachkar, 46, has pleaded not guilty to charges of first-degree murder and dangerous driving in the officer's death.
In a Toronto courtroom on Tuesday, Logan Bodera told jurors that Kachkar was worried about taking a bed from someone else on a cold winter night.
Later that night, Dennis Gayle spoke to Kachkar. He described him as being anxious, nervous and shaking.
Gayle said Kachkar wanted to call the RCMP.
When asked why, Gayle said: "He didn't know but he thought he might do something bad."
Bodera, who has a master of arts in counselling psychology, said it was clear Kachkar had mental health issues.
After hearing testimony from the shelter workers, jurors saw video showing Kachkar rushing out of the shelter.
Barefoot and wearing a sweater, the video showed him leaving by a back door and running through a snowy parking lot.
Hours later, Kachkar would steal a snowplow leading to the fateful confrontation that killed Russell on Jan. 12, 2011.
The 11-year police veteran was 35 years old at the time of his death. Russell left behind a wife and young son.
The trial continues on Thursday.