N Sasikala, 38, and her 7-year-old son were found dead in their home in New Jersey last Thursday.
Hanumantha Rao's "movements are not restricted in any way by the criminal justice system," according to Joel Bewley, the Burlington County Prosecutor's spokesperson, quoted by a local channel in the US. "He has not been charged with a crime."
Mr Rao had reportedly told the police that he discovered their bodies when he returned home from work at night. He had a strong alibi, according to reports.
The channel said that the husband is expected to attend the funeral in India of his wife, Sasikala,38, and son Anish,6, who were found stabbed to death on March 23 in their Maple Shade home.
The spokesperson told the channel he would not comment on whether Mr Rao is a suspect because his office does not comment on past, present, or future suspects.
The source reportedly confirmed that Hanumantha Rao "was involved in a relationship with another woman as of last week". The woman was not identified.
Mr Rao and Ms Sasikala both were software professionals and had lived in the US for 12 years. She worked from home and reportedly picked up her son from school before they headed home.