The pamphlet, which was distributed to voters, appeared to have been issued on behalf of a Lib Dem councillor.
The literature urged voters to back Anna Pascoe, councillor for Camborne South ward, West Cornwall, in local elections on June 4.
But the material also implied that one of her opponents, town councillor Stuart Collimore, was not a suitable candidate.
The leaflet began: "Anna Pascoe has a strong record both on Camborne Town Council, and Kerrier District Council, of listening to local residents.
"She has always campaigned on behalf of the people she represents - rather than using her position as a personal platform (like that greasy-haired ---- Stuart Cullimore)."
The election newsletter, complete with pictures of Ms Pascoe out on the campaign trail, is understood to have been delivered to households in Camborne over the weekend.
Furious recipients immediately condemned the language used and claimed those responsible had "lost their minds".
On one local news website, a householder wrote: "I have seen an actual copy of this leaflet and all I can say is that it looks as if the Liberal Democrats have finally, utterly, and irrevocably lost their minds, gone over the edge, and fallen into the depths of insanity.
"This offensive and shameful Lib Dem leaflet has been widely distributed around Camborne and many voters are said to be outraged by the embarrassing and highly distasteful behaviour of the Liberal Democrats."
Ms Pascoe expressed her shock at the leaflets and denied she had been involved in their printing or distribution. At least 40 leaflets are known to have been delivered.
She said: "I categorically wish to state that the comments were not made by myself or authorised by myself or the Liberal Democrat Party.
"We have begun a full investigation into who may have produced and distributed this leaflet."
Ms Pascoe's agent, Joe Taylor, claimed that the leaflet had not been authorised but was instead "some kind of prank that's back-fired".
He said he had been responsible for printing a similar leaflet, which did not contain the abusive comments, and that a volunteer may have adapted the original without consent.
He said: "I am absolutely outraged about this myself. What's particularly distressing is that we took the decision to fight a positive campaign. We think the offending leaflets were distributed by one of our volunteers."
Mr Cullimore, who is standing as a candidate for the Mebyon Kernow party, said yeterday: "The Lib Dems must obviously investigate.
"The leaflet is exactly the same Liberal Democrat format which they use and it's got the same pictures of her (Ms Pascoe) that they always use.
"If they are suggesting that they did not come out from an official Liberal Democrat source then it's a matter for the police in my opinion.
"From what I've heard, the person who distributed the leaflet was a Liberal Democrat worker."
The other candidates running for the Camborne South ward are: Jacqueline Harding - Labour, John Herd - Conservatives, and John Woodward - Independent.
