One of the family members said that Singh was taken to Patna Medical College and Hospital (PMCH) after his condition deteriorated, but the doctors declared him brought dead.
Ayodhya Prasad, a kin of Singh, alleged that Singh's body was kept in the open, outside the hospital, as the hospital management kept them waiting for an ambulance for over two hours.
However, after the news of the mathematician's death spread, an ambulance was provided to take the body home.
Expressing grief over Singh's death, Bihar Chief Minister Nitish Kumar said he had made Bihar and India proud. His death has caused an irreparable loss to the state and the country.
Kumar said that Singh will be cremated with full state honours. The Chief Minister then visited Singh's residence in Patna and paid tributes.
Born on April 2, 1942, Singh had been suffering from schizophrenia for nearly four decades.
Singh, a resident of Basantpur in Bhojpur district, was shifted to PMCH last month. However, he was discharged after treatment.
The mathematician is said to have challenged Einstein's theory of relativity.
Singh did his schooling from Netarhat Residential School. In 1962, he passed Class X.
Later, while studying at Patna Science College, he met American Professor Kelly, who invited him to Berkeley, US for research.
In 1963, he went to California University for research. In 1969, he received a Ph.D. degree from the varsity. His research on Cycle Vector Space Theory made him famous.
After completing his studies, he returned to India.
Later, he joined as a mathematics professor in Washington. In 1971, he came back to India. He worked at the Indian Institute of Technology (IIT), Kanpur and IIT, Kolkata.
In 1974, he began suffering from several critical illnesses.
( With inputs from IANS )