(KHNL) - Governor Linda Lingle also has issues with a bill that would provide immunity to anyone who abandons a newborn baby.
She is worried about the rights of fathers, as well as the rights of extended family members.
The so-called "safe haven" bill would allow anyone to drop off a newborn at a police station, fire station, or hospital - no questions asked and with no threat of prosecution.
It's meant to discourage mothers from abandoning their babies.
But the governor says her concern is making sure the children haven't been taken from their parents unknowingly.
Another measure on the governor's hit list would divert money from the tobacco prevention and control fund to the University of Hawaii medical school's operating expenses.
Lingle says the money should be kept - to stop people from smoking.
Another bill would cut funds for parks statewide by re-allocating a portion of the admission fees at Diamond Head, for use at only that location.
The governor says this would negatively affect repair and maintenance at other parks.