Ms Otieno, a student at Rongo University, was murdered and her body dumped in a thicket in Homa Bay last week.
Speaking to the Nation at Rapogi High School in Uriri Sub-county, Migori County on Sunday, Mr Okuta said he believes the killers will be known.
Although he confirmed that Ms Otieno was married to him, he declined to speak about their marriage, saying that the matter is too emotive for him to comment on.
When the Nation visited the school, Mr Okuta, a dark-complexioned, middle-aged man about five feet tall was wearing shorts and busy with the students.
He was initially hesitant to speak to the media and only spoke after a colleague joined him.
He was terse but was calm during the interview, which lasted less than 10 minutes.
“This matter is too emotive for me to comment. If I wanted to comment about it, I would have done so long ago. I would rather leave the matter to the police and other investigators to find out what happened. That is all I can say,” the soft-spoken Mr Okuta said.
He maintained that the family spokesperson, Mr Joshua Okong’o, had said all that was necessary.
“What the spokesperson of the family said about the family of the deceased is enough. I will not say anything. Please go and talk to the police for more information,” he said, then left for the staffroom.
Mr Okong’o had revealed that Ms Otieno had been married to Mr Okuta, and they had a son and two daughters.
“Her husband is a high school teacher,” Mr Okong’o said, adding that the couple lived in the school compound.
Mr Okuta comes from Kamagambo in Rongo Sub-county, Migori County, and has been teaching at Rapogi High School for the last four-and-half years.
He graduated from the University of Nairobi with a bachelor’s degree in education in 2013.
Sources said that Mr Okuta and Ms Otieno separated last year.
At the time of her death, she was living with her parents in Homa Bay County.
“The two separated a few months after Sharon joined Rongo University. They separated due to marital problems and Sharon relocated to her parents’ home,” said an employee at the school, who requested anonymity.