Tensions between communities, more road congestion and potentially higher utility bills have been identified as post-Brexit possibilities in Wakefield.
The council's chief executive Merran McRae said officers were working "constantly" to assess the impact of leaving the EU on the area.
But she added that little was certain until the UK had struck a deal to leave, or it became clear it was leaving without a deal.
The authority has set aside £5million in reserves to cope with any wholesale changes after March 29, the date Brexit is set to become reality.
At a meeting of scrutiny committee chairs on Monday, Ms McRae was asked if she knew what impact Brexit could have on the area.
In response, she said: "Not really, because a lot depends on the deal we get, and whether there's a deal or a no deal.
"The main issues that have been identified as a risk across the region is transport and highways, and the knock on effects on the ports.
"(There's) Also, potentially an impact community tensions depending on whether there's a deal or a delay.
"We've got a team of officers constantly looking at things every week."
Data given at the meeting on Monday suggested that around exactly half of Wakefield residents believe that communities get along well with each other in the district.
Ms McRae said that the effects on the NHS in the district, which employs a high proportion of EU workers, wouldn't be known for another 12 months.
But she said that the council may give financial help to businesses struggling to cope with life outside the EU, but only if the effects aren't long-lasting.
Ms McRae added: "Part of the reason why we've got a contingency - and this is purely hypothetical - is that if there's particular sectors or small businesses who suffer short-term effects, we might choose to do some temporary support, just to get them over that hump.
"On the other hand, if it's a long-term hit (they have to take) we might not be able to do that.
"In terms of the day-to-day running of the council, I don't think Brexit will be hugely significant.
"I think it will be more about how we as the main organisation responsible for the place ends up having to spend money.
"One thing might be around costs of supplies, so if electricity or fuel goes up. That will affect our budget going forward, as it will on any other organisation."