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A U.S. Air Force member was arrested at his base in Arizona on Tuesday in the murder of a Mennonite woman who disappeared from her New Mexico home at the end of January, authorities said Wednesday.

Mark Gooch, 21, an airman first class, was arrested at Luke Air Force Base in Glendale and booked at the Maricopa County Jail on charges of premeditated first-degree murder, first-degree murder during the commission of a crime, kidnapping and theft in connection with the disappearance and death of Sasha Marie Krause, according to the San Juan County Sheriff's Office in New Mexico.

Sasha Krause. San Juan County Sheriff's Office

Krause, 27, was last seen leaving her Crouch Mesa, New Mexico, home at 8 p.m. on Jan. 18. Her body was discovered in Coconino County, Arizona, more than 270 miles away, about a month later.

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San Juan County Sheriff Shane Ferrari said the case was peculiar from the start because Krause disappeared from a "very secluded" Mennonite community that revolved around a church and a bookstore.

"They have a business, they live on site, and we never respond there very often for anything, so it struck us as very odd that we had someone missing, especially because you see them out in a group and having someone gone was very strange to us," the sheriff said.

After Krause's body was found, the investigation was considered criminal, and a $50,000 reward was offered for information in the case.

"Over the last few months, San Juan County has lived in fear, not knowing if we had a predator living inside of our community or somebody that was preying upon it," Ferrari said Tuesday. "I can assure you, we have our man."

Mark Gooch, 21, an Airman First Class with the U.S. Air Force. San Juan County Sheriff's Office

"The Sheriff of Coconino County and I are committed to making sure that Mark Gooch receives a max sentence for these horrible crimes, and yes, Arizona still has the death penalty," Ferrari said in a video statement. "We have the right person responsible for this horrendous crime."

A statement from the Coconino County Sheriff’s Office said its investigation determined "during the time Sasha Krause went missing, Gooch had traveled from Luke Air Force Base, where he lives, to Farmington, New Mexico," and "further investigation placed Gooch near Sunset Crater in Coconino County where Krause’s body was located."

It's unclear if Gooch has a lawyer. Neither the U.S. Air Force nor a representative for Luke Air Force Base immediately responded to requests for comment.