The expense of the genetic testing shall be paid by the party who requests the genetic testing, except that the court may apportion the costs between the parties, upon request. When the genetic testing is requested by the party seeking to establish paternity and that party is found to be indigent by the court, the expense shall be paid by the public agency providing representation; except that where a public agency is not providing representation, the expense shall be paid by the county in which the action is brought. When the genetic testing is ordered by the court on its own motion or is requested by the alleged or presumed father and that father is found to be indigent by the court, the expense shall be paid by the county in which the action is brought. Any part of the expense may be taxed as costs in the action, except that no costs may be taxed against a public agency that has not requested the genetic testing.