Police forces currently have 35 days to respond to an application under the scheme, which allows people to know whether their partner, or the partner of a loved-one has a violent past.
Rosie made an application about her boyfriend Ben Topping 11 days before he murdered her, but never heard back from Lancashire Constabulary.
It has since been revealed that he had a history of violence.
Her family say tightening up Clare’s Law was “the only positive that we can try and achieve from this”.
>>>Sign the petition by clicking hereRosie’s sister Alice said: “We’re really pleased with the support so far, but we can’t rest on our laurels, we need to keep this going.”
Ribbleton Councillor Brian Rollo has signed the petition.
He said: “There is a real sense in Ribbleton that something positive needs to come out of this, but also wider too.
“The length of time needs looking at, but I can understand that the police are struggling with numbers.
“It’s a question of priorities, but this needs to be raised up the priority list.”
The aims of the petition are:
- A reduction in the 35-day timescale for applications to be resolved
- A 48-hour callback from the police to update the applicant on the process after first contact
- A national database containing details of people charged with or convicted of violent offences
- A publicity campaign on what Clare’s Law is and how to apply.
>>>Click here for Rosie's story