Smith paid tribute to Karen Dow, saying she should have been celebrating her son's birthday today.
"I can't think of anything as tough as losing a child, and all the worse for the tragic circumstances that occurred New Year's Eve before last," Smith said.
He said Matthew Dow was the 79th person that year to be killed by a drugged driver, a number higher than those killed by drunk drivers.
Karen Dow launched the petition at the site of the crash on the first anniversary of her son's death last year.
"New Zealand urgently needs to introduce roadside drug testing to address the increasing road toll and to protect motorists from the effects of the Government's reforms that allow easier access to drugs," Smith said.
"The current law and enforcement for drug-impaired drivers is ineffective and weak, compared to that for drunk driving."
Smith said saliva tests worked well in Australia, the United Kingdom and Canada, and were urgently needed here, he said.
It is simply not good enough that every five days in New Zealand, a person like Matthew Dow loses their life to a drugged driver."
Karen Dow said her son was very safety-conscious. "I was very proud of that."
"He had an immense sense of justice and this is another reason why it's important for us as a family to try and do right by the rest of New Zealand, to prevent any other family from losing a family member.
"It was no accident. It was basically murder. He had no chance to avoid having been hit head-on from a reckless driver.
"I just want to see justice done in a democratic way."
Both Smith and Dow criticised Police Minister Stuart Nash, saying he made misleading comments during an interview about the issue on New Year's Eve last year, the first anniversary of Matthew's death.
Nash told TVNZ at the time that a discussion document had been approved by Cabinet and would go out to the public early this year.
Nash said today that Smith had never approached him about the Dow case or about drugged driving generally.
"I gave a media interview at New Years where I indicated Cabinet has approved in principle the release of a discussion document. Since then the discussion document has been under preparation," Nash said.
The release of the document was imminent, he said.