The Celebrity Big Brother star, who has battled alcoholism in the past, was spotted lying on the grass after drinking vodka.
She also smoked cigarettes and later appeared to vomit in the public space, according to The Sun.
Before she left Studio City park alone, she reportedly drank mouthwash in a bid to disguise the smell of alcohol on her breath.
Nielsen checked into rehab in 2007 after an apparent intervention by family members.
She has since released an autobiography and was most recently linked to I'm a Celebrity... Get Me Out of Here!.