A one-year-old boy and his 42-year-old father died in the incident on Monday morning in St-Liboire, east of Montreal, police said.
"We have car-collision specialists who are here to try to establish exactly what happened where the impact took place," provincial police spokeswoman Joyce Kemp said Monday.
"We cannot exclude that this could be a voluntary act and, for that reason, the investigation has been transferred to the homicide squad."
Kemp said the infant was declared dead after being transported to hospital.
Later on Monday, another provincial police spokesman said the two victims, who lived in the area, were father and son.
Sgt. Claude Denis identified the victims as Thierry Patenaude-Turcotte and his son, Nicolas Turcotte.
The impact of the collision was so violent the SUV was cut in two.
Kemp would not confirm that the barriers at the crossing were working properly at the time, although a Via spokesman said the barriers were down and that the lights were flashing.
"Via Rail had no prior information that there was anything wrong with this crossing," Jacques C. Gagnon said in an interview.
"There were some tests done after the accident...we had a train ride in both directions to ensure that the automatic warning devices were working properly and it was confirmed afterwards."
He pointed out that the track is owned by CN, which carries out maintenance and preventive work.
Gagnon also said there was a camera on board the Quebec City-bound train, which left Montreal at 6:15 a.m. — about an hour before the incident.
"Everything will be transferred to the competent authorities, the Transportation Safety Board, which will determine the circumstances and the exact cause," he added.
The TSB said Monday it had sent a team to the scene of the incident, which caused delays on Via's Montreal-Quebec City route.
Gagnon said some 700 Via passengers were affected and that buses were chartered to allow them to get to their destinations.
While the circumstances of the current case remained unclear, the issue of passenger trains colliding with vehicles is a major safety issue, according to the board.
In the past decade, there have been 257 accidents involving cars and passenger trains, including 71 in the Quebec City-Windsor corridor, Canada's busiest rail route.
— With files from Peter Rakobowchuk in Montreal