Initial inquiries by Kent Police have so far found "no evidence" of electoral fraud in Thanet South, the seat that Ukip's Nigel Farage failed to win at the general election.
The force was contacted by a member of the public on Monday after Mr Farage lost out to the Conservatives' Craig Mackinlay, who racked up 18,838 votes to Mr Farage's 16,026.
On Monday May 11, Kent Police was contacted by a member of the public from outside the county around election fraud due to speculation on social media in South Thanet.
Initial inquiries by officers have been carried out and so far no evidence of electoral fraud has been found.
Kent Police has received a report of electoral fraud. Inquiries are ongoing.
Police are looking into an allegation of electoral fraud in Thanet South, the seat which Ukip leader Nigel Farage failed to win at the general election.
Mr Farage lost to the Conservatives' Craig Mackinlay who won 18,838 votes to Mr Farage's 16,026.
A Kent Police spokesman said: "Kent Police has received a report of electoral fraud. Inquiries are ongoing."
Farage quit as Ukip leader after the result, but his resignation was rejected by the party and he remains as leader.
Ukip's National Executive Committee has denied coming under pressure from Nigel Farage to reject his own resignation and said the body was "100% behind" the leader.
It comes after reports suggested Farage was in the room for deliberations about the party leadership.
Chairman Steve Crowther said: "There was not the slightest suggestion that the NEC was anything other than unanimous in its wish for Nigel to withdraw his resignation.
"He spent a considerable time making the case for his resignation, and the appointment of an interim leader, but there was no-one in the committee who did not want him to stay on.
"He left the room while it was further discussed. I took the views of members and they unanimously asked him to remain as leader. The NEC is 100% behind Nigel as we go forward in to the referendum campaign which is already under way."
Nigel Farage has denied that Ukip is a "one-man band" after his surprise return as leader - just three days after resigning.Read the full story ›
Ukip's Nigel Farage has revealed he felt he "owed it" to the party to stay on as leader when the national executive committee rejected his resignation.
In a first-person piece written forThe Telegraph, he said he felt there were "huge battles about to take place", adding that he had to put the country's interests first and foremost - as well as honour the wishes of the party's members.
Ukip will focus on electorial reform, he said, highlighting the four million votes they won - returning just one MP to Parliament - compared to the 56 SNP MPs elected on just 1.4 million votes between them.
And the major issue on the horizon, he added, was the promised referendum on Britain's membership of the EU.
As much as I wanted to spend the summer fishing, walking, and of course, in the European Parliament where all hell is currently breaking loose – that I owed it to the party that got me here.
There are some huge battles about to take place, and as much as I had thought that taking at least the summer off was in my best interests, I realise now that the party comes before me, and indeed, that this country comes before both.
With a European Referendum potentially on the horizon, I feel the need to stay involved for just a little bit longer, to add my voice to those who want Britain to be a country that trades and deals with the world, rather than ties itself to a post-WWII mind set about Europe and the political union.
Have I done the right thing by my party and my country? I think so. And I’m sure many people will have their opinions on the matter. All I can say is that I’m ready for the challenges ahead.
The fight starts here.
Senior Ukip members have welcomed Nigel Farage's decision to stay on as party leader, after the national executive committee rejected his resignation.
Deputy chairman of the party, Suzanne Evans, had been tipped to stand in until a leadership contest in the autumn - but she took to Twitter to assure followers she was among those who helped persuade Mr Farage to stay.
Very pleased @nigel_farage still at the helm. As stated previously, I tried to persuade him to stay and was never actually appointed leader!
It comes after a statement by party chairman Steve Crowther was released, explaining that the committee had rejected the resignation on the basis that Ukip members did not want Mr Farage to leave and labelling the election campaign a "great success".
Nigel Farage remains the leader of Ukip after his resignation was rejected by the party's national executive committee, Ukip has said in a statement.
Ukip chairman Steve Crowther said the committee (NEC) had produced "overwhelming evidence" that members of the party did not want him to go, saying they believed the general election campaign had been "a great success".
He said Mr Farage had been "persuaded" by the committee to withdraw his resignation.
We have fought a positive campaign with a very good manifesto and despite relentless, negative attacks and an astonishing last minute swing to the Conservatives over fear of the SNP. In these circumstances, four million votes was an extraordinary achievement.
On that basis Mr Farage withdrew his resignation and will remain leader of Ukip.
In addition, the NEC recognised that the referendum campaign has already begun this week and we need our best team to fight that campaign led by Nigel.
He has therefore been persuaded by the NEC to withdraw his resignation and remains leader of Ukip.
Mr Farage had announced before the election that he would resign if he was not voted into his chosen constituency of South Thanet - and he duly did so on Friday afternoon.
However, he had kept the option of returning open by hinting he might compete in the leadership race in the autumn.
Nigel Farage has repeated his attack on the first-past-the-post voting system, saying he felt the 3.8 million voters who backed Ukip should be better represented.
Writing in the Independent,he said: "It is my view that the first-past-the-post system is now totally bankrupt. It has turned general election campaigns into "please vote for me, I'm not quite as ugly as the other one" situations, rather than parties fighting over policy positions and serious issues. It has directly led to a campaign of total negativity and triviality.
Mr Farage also said he would "think seriously" about his next move, and hinted he wanted to play a role in an referendum on the EU.
He said: "I say that, though it nags in the back of my mind that this majority Conservative government has promised a referendum on Britain's EU membership. I guess I face some tough decisions."