Instead detectives believe the 14-year-old sent herself abuse messages on the popular social networking website.
Hannah was found dead at home in Lutterworth, Leicestershire, last August.
Dozens of abusive anonymous messages were found on Hannah's Ask.fm profile following her death - raising fears she had been targeted by trolls.
But during a pre-inquest review into her death it emerged there was no evidence she was the victim of trolling.
Coroner Catherine Mason said Ask.fm would not be represented at the inquest because there was no evidence the messages were sent by trolls.
She said: "I want to hear from the police about what they found out about the use of the computer by Hannah.
"When all this started there was real suspicion and concern that there was trolling.
"What I now know on all of the evidence I have before me is that in relation to Hannah, I do not have that evidence.
"Therefore I can't explore the issue of trolling."
Hannah's father Dave, 45, revealed after the hearing at Leicester Town Hall that police told him Hannah sent the anonymous messages to herself.
However, he said he still believed Hannah had received postings from other Ask.fm members.
Mr Smith added: "I don't think all the messages she received were sent by herself. But the police won't let me have the computer or her phone back, so I can't prove anything."
At the time of the tragedy, Mr Smith welcomed safety improvements made by Ask.fm, but added: "They have only done what they have done because of the stink I have created.
"They had no option but to act because of the public outcry after hearing how Hannah was bullied for months online on Ask.fm."
A full inquest into the teenager's death - which led to Latvia-based Ask.fm announcing a raft of safety changes - will take place in May.