The hearing is part of a death row case that questions whether doctors can be punished for participating in a state execution.
Some people like Wayne Uber believe there are times when the death penalty is appropriate. His brother's killer has two life sentences.
"If it had been my choice, the man who murdered my brother would have been executed," Uber said. "Because as long as this man lives, he represents a danger to everyone around him."
But the state medical board does no want physicians to participate in executions.
In the case of the Department of Correction versus the medical board, the supreme court heard lawyers cite a code of ethics that precludes doctor involvement in capital punishment.
The state says doctors are needed to monitor an inmate's vital signs at the time of execution and to certify an inmate's death.
"If all they were doing was certifying death, that would not be inconsistent with the board's position statement," Todd Brosius of the medical board said. "But essentially, the DOC's contemplated a more active role."
The justices asked probing questions before the end of Tuesday's hearing.
They will consider both sides and Uber hopes their decision will end the effective moratorium on executions in the state. He says the medical board is wrong for threatening sanctions against doctors who get involved in executions.
"The medical board does not recognize the fact that this position puts them on the side of death row inmates," Uber said. "And that just marginalizes them."
There is no word on when the justices will make a decision. ABC 11 will inform you of that decision as soon as they make it.