Seema was working with People Living with HIV/AIDS Society (PLWHAS), an NGO, along with her husband Gyan Ranjan Prasad, who was also diagnosed with AIDS, police said.
"Seema was depressed and upset for some time. She used to complain of being socially ostracised and her fight for survival," a friend of Seema told IANS.
Police have recovered a note, which said no one should be held responsible for her death.
In July, Premila Devi (40) from Tilaei village in Rohtas district ended her life by jumping into a well, a few months after her husband Sunil Mahto died of AIDS.
She was upset over the way her family members and villagers treated her after his death.
According to a Bihar State AIDS Control Society (BSACS) official, there are 8,228 identified as HIV positive cases and 1,100 known cases of AIDS in Bihar. Over 80 people, including 13 children, have died of the disease.
The unofficial figures are higher at over 40,000 HIV positive cases and over 100 people dead.