A month ago, the Court of Appeal for western Sweden found the city guilty of ethnic discrimination and ordered it to pay the women 20,000 kronor ($3,230) each in damages.
The city had been sued by the Discrimination Ombudsman (DO).
The women, Houda Morabet and Hayal Eroglu, were at the pool accompanying their children but had no intention of swimming themselves.
Both were wearing veils, long pants and long-sleeved tee-shirts because their religion does not allow them to reveal parts of their body in public.
The life guards considered the women’s clothing hazardous as it could inhibit their ability to swim if they fell into the pool.
The District Court had ruled in favor of the city, but the Court of Appeal overturned the decision, finding that the women were subject to discrimination when the life guards demanded the women change clothes or leave the swimming pool area.
The city is now asking for a hearing in front of the Supreme Court.