It is understood the Liberal MP, who died in 2010, was stopped on the M1 in Northamptonshire during the 1980s.
But he was released from police custody after making a telephone call to an unidentified third party in London, it has been claimed.
Northamptonshire Police is probing the circumstances around the arrest.
Labour MP Simon Danczuk first made the claim in his book about Smith, published last year.
He alleged Smith was stopped on suspicion of a driving offence, but quickly released after he made the phone call.
Despite being taken into the police station, the material said to have been found in his boot disappeared, Mr Danczuk said.
Northamptonshire Police has launched an investigation into the claims, the BBC has learned.
Lead officer Supt Steve Lingley said: "We're investigating it as an historic report and we want to make sure that we get the facts using the right resources.
"If Cyril Smith was stopped on the M1, and was arrested by Northamptonshire Police, I want to know who those officers are.
"We want to understand why they released him.
"We want to know if they came under any pressure, who that person was that gave the instruction to be released."
The force's Police and Crime Commissioner Adam Simmonds said the suspicion was officers were "brought under pressure from somebody in London to release Smith".
"What worries me the most about that is, if we had reason to hold onto him, this man was released back into the community and continued to perpetrate heinous crimes," he said.
Earlier this week, it was claimed an undercover investigation gathering evidence of child abuse claims in the 1980s against Smith was 'scrapped' shortly after he was arrested on a separate occasion.
A cold case unit is to investigate claims police released MP Cyril Smith after images of child abuse were found in the boot of his car.