(CNN) A faith-based group in Michigan is suing the state for refusing to work with child welfare agencies that turn away same-sex couples or others who don't share their religious beliefs.

The agency claims that, in doing so, Michigan is violating its constitutional right to religious expression.

The lawsuit was filed Monday by the Becket Fund for Religious Liberty on behalf of Michigan-based foster and adoptive services contractor St. Vincent Catholic Charities, a couple who adopted five children through St. Vincent and a woman who was adopted through St. Vincent.

"There isn't any access problem or harm in (St. Vincent) continuing to operate as they were," Becket Fund attorney Nick Reaves told CNN. "They don't stand in the way of same-sex couples."

The St. Vincent lawsuit comes after Michigan last month said it would end contracts with adoption agencies that discriminate against same-sex couples or LGBTQ people who "may otherwise be qualified foster care or adoptive parents" for children in state custody.

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