The accused and his accomplices have been arrested and two juveniles have been apprehended, they added.
The incident occurred last night. The accused, accompanied by his friends, went to the woman's house, police said.
When she came out, he allegedly shot her in the chest. Her brother was also there when she was shot. She was rushed to a hospital where she succumbed during treatment, police said.
Her family members told police that the accused and the victim were friends and few months back he had proposed her for marriage. However, she had turned down his proposal, which apparently left him angry, police said.
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The woman threatened to file a police complaint but didn't do so, police said.
Police found the mobile number of the accused Manoj on the woman's phone. He was tracked through his number and arrested from Tigri, police said.
His friend Afroz was also arrested along with him.
Two juveniles have been apprehended and the murder weapon has been recovered from one of them, police said.