The High Court will rule on Monday whether the Minister for Health, Mr Martin, spent beyond his permitted statutory limit in the 2002 General Election.
Disability campaigner Ms Kathy Sinnott claims there was an overspend and, with Mr Mark Menihane, an elector in Cork South Central, she has brought a petition seeking a fresh election in the constituency where she lost the battle for the last seat by six votes to Fianna Fáil's John Dennehy.
Ms Sinnott claims the minister exceeded his statutory limit of €38,092.
Mr Martin topped the poll in the five-seater constituency, with 5,500 votes above the quota.
If Mr Justice Kelly determines there was an overspend by Mr Martin, he will hear further evidence before making a decision on whether this had a material effect on the outcome of the election, requiring a fresh election to be called.
Mr Justice Kelly is also due to hear a separate petition brought by defeated Labour Party candidate in Wicklow, Mr Nicky Kelly, challenging the result of the general election on the basis of an alleged overspend by Fianna Fáil TD Joe Jacob.