The state's response filed Friday in federal court in Frankfort maintains providing tourism incentives to Ark Encounter would violate the state and federal constitutions.
Ark Encounter is a theme park planned in northern Kentucky around a 500-foot-long wooden ark modeled after the Bible's story of Noah.
State officials told Answers in Genesis in December that the project's mission has changed from tourist attraction to ministry and denied the application.
Answers in Genesis has argued that its application for about $18 million in sales tax rebates should be treated the same as a non-religious applicant.
