JACKSON (AP) — Mississippi officials are hoping to increase child support collections by offering free paternity testing this month.

A DNA test to establish that a man is a child’s father can cost $300 to $500. Adding attorneys’ fees can run the tab up to more than $1,000.

The state is paying the expenses because officials want to increase child support collections by the end of this month, when the federal budget year wraps up. Mississippi is trying to keep federal funding for its Department of Human Services.

Before DHS can pursue child support payments, paternity has to be established. For unmarried couples, a DNA test or voluntary acknowledgment are the only options.

DHS uses several methods to collect child support payments from neglectful parents, including withholding income, denying passports and putting liens on property. In some cases, parents can be put in jail for not paying.

Martha Benjamin, director of field operations at DHS’ Division of Child Support Enforcement, said there are reasons to establish paternity that are ‘‘much farther reaching than just the financial benefits to the child.’’

‘‘It’s been proven over and over that children who know both parents … become more productive citizens in life,’’ she said.

Jean Brooks, a social work professor at Jackson State University, said she does not think the program would work well if it were forced on anyone and parents shouldn’t see this as a quick fix.

‘‘It is useful to know who your father is as long as the father is interested in stepping up and being a father,’’ Brooks said. ‘‘The father has to be ready to assume the responsibilities of parenting and the mother needs to be willing to have the father in her child’s life.’’

Benjamin said the Division of Child Support Enforcement has sponsored similar efforts to increase collections, but this is the first time the state is covering other costs associated with establishing paternity.

During fiscal 2009, the Department of Human Services collected more than $286 million in child support payments. That was up $21.9 million from 2008.