(CNN) -- New Hampshire's state House of Representatives voted Wednesday to abolish the state's death penalty, which has not been carried out in nearly 70 years.
The bill will next head to the state Senate where its fate is not certain. However, the 193-174 vote in the Democratic-led House is well short of the two-thirds majority needed to override a threatened veto by Gov. John Lynch.
"I believe there are some crimes that are so heinous, the death penalty is warranted," Lynch said in a statement issued by his office.
New Hampshire's last execution was conducted in 1939, said Jeff Lyons, a spokesman for the state Department of Corrections.
"We haven't executed anyone since then, and back then, everything was done by hanging," he said.
State Rep. Robert "Rennie" Cushing, a Democrat whose father was a murder victim, said that history shows New Hampshire is "not in love with the death penalty." Cushing spoke Wednesday in favor of getting rid of capital punishment.
"I wanted to make it clear to my colleagues that a ritual killing, filling another coffin, was not a tribute to my father," he said. "To many survivors of murder victims, it dishonors our loved ones."
The state's only inmate now facing execution is Michael Addison, who was sentenced to death in December for killing a Manchester police officer in 2006. The bill that passed Wednesday would not affect his case, Cushing said, but "the fact that we now have someone on death row gives a certain urgency to it."
Addison's case became a politically and racially charged issue in a state that is 95 percent white. The same year Addison, who is black, went to trial, a wealthy white businessman, John Brooks, was sentenced to life without parole after being convicted in a murder-for-hire scheme with two other men.
New Hampshire adopted lethal injection as its method of execution in 1988, but hanging could still be used if doctors couldn't administer the injection for some reason, Lyons said.
New Hampshire is one of 35 states with capital punishment on the books. Texas leads the country in executions, with 435 convicts put to death since 1982. See which states have bills to repeal death penalty »
New Mexico Gov. Bill Richardson signed a bill abolishing the death penalty in his state last week, calling its application "inherently defective." Several other states, including Colorado, Kansas, Maryland and Montana, are considering changes to their capital punishment laws.
Asked about Lynch's opposition, Cushing said, "We're hoping that the governor will emulate the journey that Gov. Richardson took recently."
CNN's Bill Mears contributed to this report.
All About New Hampshire • Capital Punishment