The pair pose a "significant threat to public safety," police said.
Cara Duval, who also goes by Cara Donnelly, and Joseph Pepin, were reported missing from the North Bay Regional Health Centre's mental health and law program on Jan. 22, at about 6 p.m., North Bay police said in a statement.
The pair failed to return from permitted off-unit privileges.
Investigators have since received information that Duval and Pepin were both in Hanwell, N.B., on Jan. 27.
"Without ongoing monitoring and supervision, both pose a significant threat to public safety," police said.
The public is advised not to approach Duval or Pepin and to call 911 immediately if they see them.
Duval, 37, is described as being five feet, one inch tall, 117 pounds, with brown shoulder-length hair, usually kept in a pony tail, and brown eyes.
She was last seen wearing a three-quarter length blue coat, pink boots, and a blue and black toque.
Pepin, 39, is six feet tall, 174 pounds, with brown hair and blue eyes.
He may be wearing a three-quarter length grey coat, jeans and running shoes.
Police believe Duval and Pepin may be travelling in a 2006 dark grey Volkswagen Jetta, with Ontario licence plate BRVK449.