Call 214-670-0109 and ask to start a service request. Click here to submit an online jury service postponement request.You may also write a letter to the Jury Services Department and request a postponement. I recently received a letter summoning me to serve in a Grand Jury in Dallas County. It said something like this would take multiple days a week for 3 months. There is no time limit in which it must be served, but plaintiffs typically want them served as quickly as possible. For service on the petit jury in the Municipal Court of the City of Dallas. Jurors must enter at 2014 Main St. (front of the building) In Texas justice courts and small claims courts, you have 14 days from the date of service to file your answer. You are on call for approximately one month.