A complaint was made after an episode of the BBC show featured a gypsy character selling pegs and lucky heather and a joke about a fortune teller stealing Basil's wallet.
Gypsies from Kinsmead Close, Wiveliscombe reported the show to the Police alleging that the storyline is racist towards their community and way of life.
Michael Phillips, vice-chairman of the South West Romany, gypsy and Irish Traveller Network, called on the BBC to pull the episode and give travellers the same protection and respect they give to other ethnic minorities.
"They need to realise that gypsies and travellers are a recognised ethnic minority in this country and deserve the same treatment as any other group," he said.
"To perpetuate this myth about gypsies and travellers is wrong. Attitudes like this belong 20 or 30 years ago, we are supposed to have moved on since then.
"If they are going to keep showing this then I look forward to them bringing back the likes of Alf Garnett to the screen."
The BBC refused to comment on the situation, with a spokesman saying the matter was now in the hands of the police.
A spokesman for the Police said: "We can confirm we have received a complaint about a TV show featuring Basil Brush from a member of the public.
"The complaint was logged as an incident of a racist nature and we are now investigating."