Police say the incident unfolded in 'Outfield Pub' in East Islip just after 1 a.m.
The shooting happened when one man pressed a handgun against another man's body.
Officials say a fight broke out and the gun was discharged. A woman nearby was shot in the neck.
She is in the hospital in critical condition.
Police are still looking for the suspect, who ran off from the bar, officials said. The other man involved in the fight suffered non-life-threatening injuries.
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