Chief Minister Bhupinder Singh Hooda told reporters that they were "not averse to a CBI inquiry in the case, if that was the wish of the deceased woman's parents".
Geetanjali's family, which met the Chief Minister here, had accused her in-laws of harassing her for dowry.
The family has alleged that the harassment started from the birth of the couple's first daughter and worsened after their second girl child was born.
On Saturday, a case of murder was registered against Ravneet.
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30-year-old Geetanjali was found dead on July 17.
The post mortem report has mentioned that one bullet hit her stomach while another bullet hit the chin and pierced through her head. A third bullet was also fired which injured her neck minutely.
The judge had earlier claimed that Geetanjali had killed herself, her family members suspected a foul play.
Her brother has alleged that it is a case of murder, since as per the post mortem report, there are three gun-shot injuries and one head injury on her body.
After the incident, a Special Investigation Team had been formed to probe the death mystery.