Yonas Tegegn, the World Health Organisation's representative in Thailand, also an Ethiopian national, has been asked to report to police to answer allegations that he treated Annet like a slave, did not give her proper meals and provided only a small room to sleep which she shared with the family's pet dog.
Annet said Togan and his wife abused her and forced her to work without pay for nearly two years.
Tegegn said he would cooperate with authorities to clear his name.
Police said Lawyers Council of Thailand (LCT) had taken the housekeeper to lodge a complaint and police had so far interviewed neighbours, WHO staff and other witnesses.
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Tegegn said Annet worked as a housekeeper at his home and lived there from June 17, 2013, to March 8, 2015.
After that date she was scheduled to return to Ethiopia.
"At all times we have treated her as a member of our family, with all dignity, respect and consideration," Tegegn said.
LCT human rights advocate Surapong Kongchantuk claims there is enough evidence to indict Tegegn on four charges, including human trafficking, enslavement, confinement and confiscating Annet's passport.
"We believe that the victim provided true testimony, and we do not believe that there is any reason for her to have ill-intentions towards the accused person," Surapong was quoted by Bangkok post as saying.
He said the couple agreed to pay 2,000 birr (about 6,000 rupees) a month to Annet's family in Ethiopia, but they received only 5,000 birr for the first five months of her employment.
Surapong said under Thai law the money should have been paid directly to the employee, not his or her relatives.
"The victim has not received a single baht since her first day of work," Surapong said.
"And since she was not paid the minimum wage of 300 baht per day, we will also file civil charges against [the couple]," Surapong said.