Mitt Romney's campaign has been hit by his links to a firm providing the voting machines that will be used to tally the ballots in the crucial state of Ohio, as concerns of voter fraud increase in the tightly fought race.

Ohio is traditionally seen as the closest and most important state in a presidential election. The close contest between Mr Romney and Barack Obama could easily come down to the counts in Ohio and Florida – the latter was the scene of a bitter struggle in 2000 between the Democrat Al Gore and George W Bush. Mr Obama still has a narrow lead over the Republican challenger in Ohio, according to polls, while Florida is tilted towards Mr Romney.

Salon magazine reported on Tuesday on the "extensive corporate ties to the Mitt Romney camp" of Hart InterCivic, the voting-machine provider that will be used to count the votes in Ohio, and the other key swing states of Colorado and Virginia. Reports in the US media since the end of last month have linked the company to Mr Romney's campaign donors and his son Tagg.

The Washington Post noted that the implication is that "Romney will enjoy some kind of malign leverage over the vote count in Ohio". Hart InterCivic said in a statement that it has a "long track record of supporting a fair and open democratic process. Any suggestions that the company might try to influence the outcome of election results is unfounded".

The swirling controversy over Hart InterCivic has provided a timely reminder that it's not just how you vote but how the votes are counted that could decide the winner of the election on 6 November. In 2004, the role of voting machines came under scrutiny in Ohio where Mr Bush defeated Democratic challenger Senator John Kerry by 118,601 votes out of more than 5.6 million cast. The result was controversial because Walden O'Dell, the chief executive of an Ohio-based voting-machine manufacturer, had earlier declared his commitment to helping secure Mr Bush's re-election.

With the campaigns going after every vote and the electoral stakes so high there are already signs of attempted election fraud. Voters in Florida, Virginia and Indiana had been receiving phone calls informing them – incorrectly – that they can vote by phone on election day. One Republican from St Augustine, Kurtis Killian, told the Associated Press that he had been called by a man identifying himself as an employee of the Florida Division of Elections.

Also in Florida, where early voting begins next Saturday, bogus letters have been sent to dozens of voters telling them their citizenship is in doubt. The letters – apparently targeting Republicans – say that if they attempt to vote before clearing up their status they would risk a jail sentence.

This year, as in 2008, the Obama campaign efforts have focused on early votes that can be cast either through absentee ballots or by voting in person. Mr Obama will vote in his home city of Chicago today. But in campaign appearances this week, Mr Romney has also been urging Republicans to take advantage of an early vote in states where it is permitted.

In the toss-up state of Iowa, voters can register and cast their ballot on the same day. Timothy Hagle, a political science professor at the University of Iowa, said voting has been made easier in the state thanks to convenient satellite voting stations where people can vote regardless of whether they are registered at that precinct.

Amid what Professor Hagle called a "general enthusiasm gap" for the incumbent President compared with in 2008, Democratic activists have focused on bringing out the student vote through the Campus Takeover initiative. "Celebrities take part and then walk the students to the satellite voting stations on campus," Professor Hagle said. The singer Bruce Springsteen was among those taking part last week.

Senator's rape comments pose problems

Mitt Romney has been embarrassed by a Senate candidate from his own party who said that pregnancy resulting from rape is "something that God intended to happen".

Richard Mourdock, a Tea Party-backed candidate who is running for a Senate seat in Indiana after knocking out veteran moderate Senator Richard Lugar in a primary contest, made the remark during an election debate on Tuesday night.