The deceased, identified as Suma, a homemaker, lived in Halenahalli Layout here, they said.
Police said she had left behind a suicide note, the contents of which are being examined. However, she did not hold anyone responsible for her death.
According to police, she shot herself with her licensed revolver when no one else was at home.
Citing preliminary investigations, a senior police officer said the woman had allegedly been battling depression for the past five years and had been on medication for the condition for the past two years.
Her husband, a businessman, was away for work in Bengaluru when the incident occurred, he said.
The woman is survived by her husband and two children, he added.
The exact reason behind the death is yet to be ascertained. Her body has been sent for post-mortem examination.
The Basavanahalli police have registered a case of unnatural death, and further investigation is underway.
