What crimes district courts can handle

(a) District courts shall have jurisdiction of, and their criminal jurisdiction is limited to, criminal offenses punishable by fine, or by imprisonment not exceeding one year whether with or without fine. They shall not have jurisdiction over any offense for which the accused cannot be held to answer unless on a presentment or indictment of a grand jury. In any case cognizable by a district court under this section in which the accused has the right to a trial by jury in the first instance, the district court, upon demand by the accused for a trial by jury, shall not exercise jurisdiction over the case, but shall examine and discharge or commit for trial the accused as provided by law; provided that, if in any such case the accused does not demand a trial by jury on the date of arraignment or within ten days thereafter, the district court may exercise jurisdiction over the case, subject to the right of appeal as provided by law. (b) The district court shall have concurrent jurisdiction with the family court of any violation of an order issued pursuant to chapter 586 or any violation of section 709-904, 709-905, or 709-906 when multiple offenses are charged and at least one other offense is a criminal offense within the jurisdiction of the district courts.