The city council has refused to confirm it investigated allegations a man urinated outside the Civic Centre during the election count.
The incident was reported to Southampton officials who were overseeing the election process at the Guildhall last week.
A short response given by the council at the time intimated a candidate was involved.
Since last week, the local authority has refused to provide any further comment or response to questions.
Conservative group leader Peter Baillie said he was told the incident was reported to the council’s legal executive after a candidate who was in the car park outside the Civic Centre at the time had found the situation upsetting.
He said it “beggars belief” why anyone would act in such a way, which would have seen them go past toilets in the Civic Centre.
Cllr Baillie said: “That behaviour is totally unacceptable.
“It’s bizarre, I’ve never come across something like that.”
The Local Democracy Reporting Service (LDRS) approached the council during the count in the early hours on Friday, May 8, after receiving reports of the incident.
In a statement, a spokeswoman for the council election team said: “We are aware and we have dealt with it appropriately.
“Our priority is to focus on the smooth running of the count tonight.
“At this moment in time the individual involved is just a member of the public.”
This week the LDRS asked the council to confirm what reports it received in relation to the incident, what investigations were carried out and what did they conclude, had the matter been reported to police and what support had been provided to anyone affected by the incident.
A council spokesman said they would not be providing a comment on the matter.
It is understood by the LDRS the council has decided to take no further action in relation to the incident.