If the claims are true, it would mean Mr Montesinos fled less than a week after returning from temporary exile in Panama.
Mr Montesinos fled by yacht to the Galapagos Islands, and from there to Costa Rica, Anel Townsend said.
By way of proof, she played a videotaped interview with three officials who said they had been bodyguards to Mr Montesinos on the journey.
If the claims are true, it would mean Mr Montesinos fled less than a week after returning from temporary exile in Panama.
His return precipitated the political crisis that brought down President Alberto Fujimori after 10 years in power.
Mr Montesinos was a key player in a bribery scandal linked to Mr Fujimori, and is also accused of links with drug dealers and death squads.
Coup fears
Many Peruvians feared his return from Panama in October heralded a coup, and when he vanished, Mr Fujimori personally led a high-profile manhunt for his former henchman.
The men who say they were his bodyguards now say he fled Peru by sea on 29 October, arriving at the Galapagos six days later.
An attempt to charter a private plane for him failed, they said, so they continued by boat to Costa Rica.
The Costa Rican Government has said it will investigate that claim.
Circumstantial evidence
Ms Townsend said stamps in the mens' passports seem to support their story.
It is not clear if Peruvians believe the story, but the BBC correspondent in Peru says it is no more implausible than many other tales circuclating about Mr Montesinos.
The Montesinos crisis helped force President Fujimori from power less than a year after he was elected to a constitutionally-questionable third term.
Mr Fujimori, who is of Japanese descent, fled to Japan and is resisting being returned to Peru.
His successor, Valentin Paniagua, has fired many military and judicial figures considered loyal to Montesinos, and has said trying the former intelligence chief is a priority.