The 49-year-old was remanded in custody by consent rather than applying for bail and will appear again in court later this month.
When asked if she comprehended what was happening, Smith was unclear.
"I don't understand that. What does that mean?"
Her lawyer said she would discuss matters further with her.
Smith's ex-partner and children said she had become progressively more distant in recent years and had shown up at their home for Mother's Day at the weekend without warning.
They said they had called police because she was "doing our head in".
Smith, they told the Otago Daily Times, had been turning the power on and off, overturning family photos and covering mirrors.
Her ex-partner said the defendant's paranoia even stretched to the dogs.
Smith's son said two female officers arrived at the house and trespassed her from the address.
The defendant allegedly asked her daughter to make a coffee, half of which she drank. When she topped it up with more water and continued to drink, the officers said she was breaching the trespass order and went to arrest her. The alleged assault then took place.
"I got a bit of a shock because when I walked my mum out to the car with the cop the other chick ran right out to her driver's door and she was squirting a drink bottle in her face. I didn't realise [the coffee] was that hot."
Six more police cars arrived at the scene, witnesses said.
Smith would be at Christchurch Women's Prison for the foreseeable future.
"She doesn't need to be in prison, she needs to be in Wakari [Hospital]," her ex-partner said.
