In an interview, screened live yesterday, Boulton accused Campbell of ‘not caring' about the country.
Boulton also asked Campbell if it is in the public's interest that Gordon Brown remains in office for a further four months.
Campbell then accused Boulton of being upset that David Cameron was not the Prime Minister, to which Boulton became visibly angry and replied: ‘I'm not upset, you are, you keep casting aspersions.'
Ofcom confirmed it had received a number of complaints and was looking into the situation, but was not presently investigating.
The development follows complaints made following an interview by another Sky News presenter Kay Burley earlier this week. Burley received criticism for her agressive questioning of the leader of campaign group 38 Degrees, David Babbs.