The House voted 234-95 Wednesday to study the proposal that had divided gay rights advocates because it did not cover transgender individuals.
The passed the Senate unanimously, but got mixed support from witnesses testifying at a House hearing. Most argued there is no clear definition of sexual orientation and said the proposal needed to be studied before being put before voters.
The constitution currently prohibits discrimination based on race, creed, color, sex and national origin.
The amendment would have added sexual orientation and make New Hampshire the first state to single out gays for constitutional protection.
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