Bhoomika Kochhar, 25, was found dead on June 15 at her husband's house in Chundevi village of Kathmandu. She was married to Nepalese citizen Akash Jatiya in January 2011.
Police said Bhoomika and Jatiya had not been on good terms in the recent past but did not give details.
Jatiya and his family claim that she committed suicide by hanging herself but this was challenged by her father Chander Mohan Kochhar, who lives in the US.
There is no facility in Kathmandu to conduct such tests.
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Kochhar has also lodged an FIR against Jatiya, his father Anil and mother Neeta with the Metropolitan Police Circle in Kathmandu.
US Congressman Steve Israel has warned that he will call for a hold or a suspension of all or part of USD 27 million financial assistance to Nepal until the US Embassy can certify that there was an investigation into the woman's death and that it was full, fair and honest.
Jatiya is the grandson of renowned businessman Chauthamal Jatiya.
Police said they were weighing alternatives to conduct a test for blood poisoning to crack the mystery surrounding Bhoomika's death.
Senior Superintendent of Police Bijaya Kayastha told reporters yesterday that police had sought the opinion of the Attorney General to ascertain if it was legally valid to send a toxicology sample to the US for tests as requested by Bhoomika's father.
"We had sent the samples to the Central Police Forensic Science Laboratory which, said it was not equipped with the facility to test blood poisoning," he said.
Born in India, Bhumika grew up in the US.
Her father has also written to the Gender Empowerment and Coordination Unit at the Office of Prime Minister and Council of Ministers and the Ministry of Home Affairs, demanding fair investigation and justice.
"We have not established the death as suicide and police have kept all options open for free, fair and impartial investigation," Kathmandu Police chief Subodh Ghimirre said.