New legislation to help police deal with cases of abuse on Twitter is unnecessary, according to a BBC Radio 4 report quoting senior police officers.
The BBC has cited recent examples of offensive tweets aimed at Olympic diver Tom Daley and Bolton footballer Fabrice Muamba.
Stuart Hyde, of the Association of Chief Police Officers (ACPO), is quoted as telling BBC Radio 4’s Today programme that forces should take a "common sense" approach.
The Police Federation, which represents rank-and-file officers, is quoted as saying that police could not be expected to investigate every instance of abuse on Twitter.
Cumbria Chief Constable Hyde, who speaks on e-crime for ACPO, said police should get involved if people's lives were being made a misery.
However, asked if new laws were needed, he told BBC Radio 4's Today programme: "No, I think we have got quite a lot of legislation, dating back to the Malicious Communications Acts of 1998 and 2003. There is a lot there that helps us and gives us the power to do stuff.
"This is a new technology, a new way of communicating, it has grown exponentially. There hasn't been separate legislation so we are using legislation that wasn't particularly created for this but it works reasonably well most of the time."
He continued: "We are learning from it, there are things that have sometimes gone wrong and I think sometimes it is important that we make sure we provide the service people need.
"If people come to us and say 'I am really upset, I've been offended, my life has been made a misery and I want somebody to do something about it', then yes the police should, whenever possible, try to help.
"It is important to look at the whole context. It is not just about one tweet; it is a whole range of tweets. Look at what the individual has done - is this a concerted attempt to have a go at one individual in a way that passes the threshold for offences against the law? If it is, then clearly we should intervene and do something to stop it."
He urged Twitter to play its part in policing its own site.
Police Federation spokesman Steve Evans told the BBC: "The sheer scale of it is huge. Police resources are stretched almost to breaking point so if we started trying to investigate every instance of stupidity within Twitter then we would be really pushed.”
Earlier this year Twitter’s chief executive Dick Costolo said it would introduce measures to help curb the proliferation of "hate speech" and so-called trolling on its service.
"The reason we want to allow pseudonyms is there are lots of places in the world where it's the only way you'd be able to speak freely," he said.
"The flip side of that is it also emboldens these trolls. How do you make sure you are both emboldening people to speak politically but making it OK to be on the platform and not endure all this hate speech? It's very frustrating."