Does the regional department have the right to demand DNA samples without anything to compare with?

Yes, he has the right, but only if there is a corresponding decision of the investigating judge or with the voluntary consent of the person.

According to Part 3 of Art. 245 of the Criminal Procedure Code of Ukraine specifies that the collection of biological samples from a person is carried out according to the rules provided for in Article 241 of this Code. In the event of a person's refusal to voluntarily provide biological samples, the investigating judge, the court, at the request of a party to criminal proceedings being considered in accordance with the procedure provided for in Articles 160-166 of this Code, has the right to allow the investigator, the prosecutor (or oblige them, if the request was submitted by the defense ) to forcibly collect biological samples.