Sgt. Peter Thiessen said one of those rumours is an "unfounded allegation" identifying a man purported to be the tormentor of the 15-year-old.
Todd took her own life last week after enduring years of Internet sexual exploitation and bullying by her peers.
The outpouring of support and information has been overwhelming, and thousands of tips have come in, police said.
"The Internet and social media were central to Amanda's story and they are central to our investigation as well," Thiessen, spokesman for the Lower Mainland District RCMP, said in a statement.
"One of our big challenges right now is false information that is being spread by people who appear to be trying to use Amanda's story to do harm or make a profit."
Todd died last Wednesday, a month after she posted a video on YouTube that described the webcam incident that set her down a path of anxiety, depression and drug and alcohol abuse.
During the emotional nine-minute video, the teen explained in hand-written notes that she was in Grade 7 when she was lured by an unidentified male to expose her breasts during a chat.
A year later she said she received a message from a man on Facebook threatening that if she didn't give him a show, he would send the webcam picture to her friends and family.
"He knew my address, school, relatives, friends, family names," she wrote.
Over Christmas break there was a knock on her door at 4 a.m.
"It was the police... my photo was sent to everyone," she wrote. "I then got really sick and then got anxiety, major depression and panic disorder."
In the video that has now been viewed more than 8.5 million times, she outlines more recent bullying over her relationship with a boy that escalated to an assault that left her lying bloodied in a ditch.
She said she tried to kill herself twice.
"I have nobody. I need someone," she wrote at the end of the black-and-white video.
An anonymous hacker group claimed they had identified Todd's tormentor, posting a name, address and contact information for the man they say stalked the teenager and distributed that photo of her at 12 years old.
The phone number listed on the site was incorrect and a person who answered the first of two email accounts listed said the account was only registered last week and it has now been deluged with emails.
A person who responded to the second email address and purported to be the man identified, said he was "insulted and utterly disgusted" about the allegation. He did say he knew Todd, and was trying to help her.
"I would never and have never done any said actions," he wrote in the email.
A person with a similar name was in court in Surrey, B.C., on Monday on an unrelated charge of sexual assault and sexual interference of a person under 16.
At court, he told CTV News that he was Todd's friend.
The Canadian Press is not identifying the person.
RCMP called the hacker posting an "unfounded allegation."
They said another rumour suggested autopsy photos had been leaked — a false story that caused Todd's family extreme stress.
There have also been a number of fake websites and accounts set up purporting to be raising funds for the Todd family.
Thiessen said donations should only be made to the Amanda Todd Trust at RBC.
"Taking advantage of a family’s grief is despicable," Thiessen said.
RCMP says they've received thousands of tips and their investigation continues into the sexual exploitation and assault Todd endured before her death.
Also on HuffPost