Del. Code tit. 29 § 5945
If any employee in the state service shall willfully refuse or fail to appear before any court or judge, any legislative committee or any officer, board or body authorized to conduct any hearing or inquiry, or, having appeared, shall refuse to testify or answer any question relating to the affairs or government of the State or the conduct of any state officer or employee on the ground that the employee's testimony or answers would tend to incriminate the employee or shall refuse to waive immunity from prosecution on account of any matter about which the employee may be asked to testify at any such hearing or inquiry, the employee shall forfeit the employee's office or position and shall not be eligible thereafter for appointment to any position in the state service.
29 Del. C. § 5945