(a) Except as provided by this section, a court may hear any reasonable sworn excuse of a prospective juror, including any claim of an exemption or a lack of qualification, and if the excuse is considered sufficient shall release him from jury service entirely or until another day of the term, as appropriate.
(b) Pursuant to a plan approved by the commissioners court of the county in the same manner as a plan is approved for jury selection under § 62.011, the court’s designee may:
(1) hear any reasonable excuse of a prospective juror, including any claim of an exemption or a lack of qualification; and
(2) discharge the juror or release him from jury service until a specified day of the term, as appropriate, if:
(A) the excuse is considered sufficient; and
(B) the juror submits to the court’s designee a statement of the ground of the exemption or lack of qualification or other excuse.

(c) The court or the court’s designee as provided by this section may not excuse a prospective juror for an economic reason unless each party of record is present and approves the release of the juror for that reason.