Johann Lamont, leader of Labour MSPs and MPs north of the border, responded to claims that a woman who raised concerns has denied she later withdrew her complaint.
The investigation was halted in September after it was said that key witnesses withdrew evidence suggesting they were recruited to join Labour in a drive by the Unite union to cram the constituency party with supporters who would back its favoured candidate in a selection battle to replace Eric Joyce.
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Ms Lamont, speaking on BBC Radio Scotland, said: "I think we certainly need to look at that because obviously there is a concern if the investigation wasn't entirely complete. Again, I say these matters are ongoing. We know that some complaints have been given to the police.
"In this process what we want to do is get beyond the point where people are claiming and counter-claiming and get to the point where again individual Labour party members are treated with respect and, more critically, we fight to get a Labour representative in Falkirk who will stand up properly for the people of Falkirk."
Party leader Ed Miliband came under pressure to publish a report into the allegations in light of claims that the union ''manipulated'' the process.
One newspaper reported that it saw emails suggesting the retraction letter of witnesses was written by Unite officials and approved by one of the figures at the heart of the dispute, Falkirk constituency party chairman Stevie Deans, who was also the union's convenor at the Grangemouth petrochemical plant until he resigned last week.
Lorraine and Michael Kane were among those who claimed that they were signed up as members without consent.
Mrs Kane has said: "I did not change the testimony. I did not change anything. I did not withdraw anything. I want all the emails to see what's what. This has been going on for months.
"I don't know what the emails are saying. I want to see everything so I know what was said and if anything was changed from what I said."
Ms Lamont rejected calls to publish the party's internal report.
"No political party when it investigates these matters publishes these reports," she told the BBC.
"What we need to do is work closely with the party locally.
"I understand how difficult it is to be a Labour party member in Falkirk now. They have been embarrassed by who was representing them. They are now frustrated by what was going on. We will work closely with them."
She insisted the party can now move on.
"It is being dealt with, the party's in special measures, we're moving to select a candidate and I'm absolutely convinced when that candidate is selected their focus will be on engaging again with the electorate, rather than the process which is currently going on which is deeply unedifying, I have to accept, which is about the Labour party fighting with itself," she said.
The Conservative party chairman, Grant Shapps, has called for the Falkirk inquiry to be reopened.
"Ed Miliband failed to stand up to the unions in Falkirk and backed down in the face of pressure from (Unite general secretary) Len McCluskey," he said.
"If he is too weak to stand up to his union bosses and tackle what he himself called bad practices, how can he stand up for hardworking people?"
Unite denies any wrongdoing by members throughout the selection process.
A spokesman for the union said: ''Specifically, Unite entirely denies any involvement in or knowledge of the forging of signatures on application forms or of any documents whatsoever; the coercing of individuals to join the Labour party, however that might be accomplished; the recruitment of individuals to the party without their knowledge or any other breach of Labour party rules.
''Unite called for an independent public inquiry into what happened in Falkirk, and we remain entirely happy to assist such an inquiry, and draw appropriate lessons from it if necessary, should one be established.''