The owner of the property involved in any proceeding brought under the provisions of this article, before the appointment of commissioners, as provided in section 38-1-105, and before the expiration of the time for the defendant to appear and answer, may demand a jury of freeholders residing in the county in which the petition is filed to determine the compensation to be allowed in the manner provided in this article. Such demand may be made in the pleadings or by a separate writing filed with the clerk. Such jury shall consist of six persons, unless a larger number is demanded by any party to the proceeding. In no case shall the number of jurors exceed twelve. Any party so demanding a larger number than six jurors shall advance the fees for such additional jurors for one day's service according to the rate allowed jurors in the district court.