This compares to the national average of 1.4 fatalities per thousand farms over the last decade.
Responding to the figures, the HSA's Pat Griffin said that for several of the years within the decade there was no fatality in Louth, and that analysis over a longer period could produce a different picture.
"There was no fatality in Louth last year and they had a number of similar results during the past decade," said Mr Griffin.
The safest counties according to the figures are Sligo and Dublin, with no fatality recorded on farms in either county over the past decade.
Meanwhile, the IFA's Tim O'Leary, who runs an extensive dairy farming operation in Cork has described the pattern in his county as "very worrying".
"I can't give a definitive answer as to why Cork is worse than any other county.
"There is a lot of farming activity in Cork. It is a very productive county with a lot of farms and a lot of dairy farms where the rate of accidents appears to be higher.
"But dairy farmers are usually full-time farmers and there must be a correlation in that. Part-time farmers are not spending as much time on their farms as a full-time farmer," he said.
"The problem with trying to resolve the high accident rate is that we cannot identify a particular item as the cause, or something that we feel will solve the problem, or reduce the number of accidents.
"There has been a lot of focus on PTO shafts and there was no fatality caused by a PTO shaft in 2014.
"There seemed to be a lot more freak accidents last year - there was a lot of them linked with bales of silage, feeding and working with livestock.
"We have to create a situation that every morning the farmer goes out the door to work they are conscious that the most important thing is to make sure that we comes in again that night - safely.
"Apart from the fatalities the number of injuries must be having a huge effect on families," he said.
Mr O'Leary said that the age structure of fatalities in 2014 was symptomatic of the industry as a vocation, with the number of children and farmers into their 80's that were victims of farm accidents.
"There was a great job done on the construction industry, but a building site is a clearly identifiable area that starts in the morning and finishes in the evening where the only people who have access are workers with safety helmets, high vis jackets, work boots, and a ticket to do a job.
"It is clearly defined in a way that cannot be applied to the average farmyard where it is a place of work and a home as well.
He said that almost half of the fatalities in 2013 were either under 18 years or over 65 years and these are categories that will not be working on construction sites.
"For the older people it is a way of life and many of them love the involvement that they had been used to all their life, but a man of 80 years will be slower to move and we have to be more conscious of that," added Mr O'Leary.