The lawsuit was filed in state district court in Travis County, which includes Austin. It says Austin has argued that its municipal building is exempt from the law under exclusions for court buildings.
Paxton's office says it responded that the city would be fined for non-compliance within 15 days.
The suit asks the court to compel Austin to follow the law — and impose fines worth $1,500 per day for not doing so as of earlier this week.