Rick Wilking / Reuters

Lieutenant Jeff Kramer, public affairs officer for the El Paso County sheriff's office, briefs reporters on the investigation of the murder of the head of Colorado state's prison system in Monument, Colo., on March 20.

Days after the leader of Colorado's Department of Corrections was shot and killed at his home, investigators are casting a wide net as they try to piece together what happened that night.

They are exploring a possible connection to a Saudi national and are trying to find a boxy, two-door car as well as a female speed walker.

The speed walker, thought to be between the ages of 35 and 50, may have been in the neighborhood at the time of the shooting.

The woman, who is not being considered a person of interest, may have made “some observations that could be valuable” to investigators, said El Paso County Sheriff's Department spokesman Lt. Jeff Kramer.

Departments of Corrections director Tom Clements was founded dead in his Monument, Colo., home on Tuesday night, apparently shot dead by an unknown gunmen after answering his front door.

Among the possibilities being explored by investigators is that the top prison official’s death could be connected to the 2006 case of Homaidan al-Turki. Last week, Clements turned down his transfer back to Saudi Arabia.

Al-Turki, a Saudi national, was convicted and sentenced to 28 years in prison for unlawful sexual contact. A judge later reduced his sentence to eight years to life. Prosecutors said he kept a housekeeper in his Aurora home and sexually assaulted her.

Investigators are aware of the recent decision, Kramer said. “We also remain open minded to all of the other possibilities as well, because we don’t want to follow one particular trail and find ourselves perhaps missing something along the way,” Kramer said.

A federal official told NBC News on Wednesday that no federal agents have been involved in the investigation. The FBI offered assistance but so far state authorities have said they have the resources they need and declined federal help.

Gov. John Hickenlooper said at a press conference on Wednesday that there was no reason to suspect that Clements’ shooting should be seen as a threat against other high-level state officials. Capt. Jeff Goodwin of the Colorado Bureau of Investigations told the Denver Post that security around the governor’s mansion and state Capitol had been tightened.

“We have a responsibility to protect the governor and his family,” Goodwin said, according to the Denver Post. “Other people at the Capitol benefit from that increased security, as well.”

"Because of the fact that Mr. Clements served in the position that he did as the executive director of the Colorado Department of Corrections, we're sensitive to the fact that there could be any number of people who could have a motive for wanting to target him," Kramer said.   

Clements oversaw more than 20,000 inmates and a budget of $737 million in his corrections department post.

Clements had written about the hazards faced by corrections officers in a message that was posted on the Department of Corrections website -- including the death of one officer in the line of duty last year.

“Corrections is an inherently dangerous career,” Alison Morgan, a spokesperson for the Department of Corrections, said on Wednesday.

“He was an inspirational leader,” Morgan said. “He had a vision for the department and was exceptional at sharing that vision with staff and inspiring the 6,000 employees of the department.”

NBC News’ Pete Williams and Andrew Rafferty contributed to this report.

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