Wyo. Stat. § 1-11-104

(a) A juror may not be excused for a trivial cause or for hardship or inconvenience to his business, but only when material injury or destruction to his property or property entrusted to him is threatened, or when his health or the sickness or death of a member of his family requires his absence. A person who has attained the age of seventy-two (72) years may be excused at his request. A person may be excused from jury duty when the care of that person's young children requires his absence. Any person who has served on a jury during a jury term shall, upon request, be excused from further jury service in that court for the remainder of that jury term and in the discretion of the court may be excused from jury service for the following jury term.

(b) For the purposes of this section:

(i) A person has served on a jury during a jury term when he is summoned to serve and he has been selected as a juror in any court within the judicial district and has taken the oath required under W.S. 1-11-201;

(ii) A person has not served on a jury during a jury term if he is disqualified for that jury term pursuant to W.S. 1-11-102 or is discharged for that jury term pursuant to W.S. 1- 11-103.