PHOENIX — The state House voted Tuesday to ask Arizona voters to let state and local police arrest people who are in this country illegally. HCR 2039 would expand the state crime of trespass to include anyone on public or private property who is in violation of federal immigration laws. Police officers could either refer the individuals for prosecution or simply turned them over to Immigration and Customs Enforcement.

 The measure also would bar the state or local governments from having any policies, official or otherwise, that prohibit police officers from asking those they stop about their immigration status. In fact, it specifically requires officers to query anyone arrested on any other law about whether they entered the country legally.

 Tuesday’s preliminary vote is not the end of the matter. The measure still requires final House action and Senate approval.

 Ultimately, though, the final decision would be up to voters. Rep. Russell Pearce, R-Mesa, designed it that way because Gov. Janet Napolitano has previously vetoed a similar plan.

 At the center of the debate is what role local law enforcement should play in dealing with the estimated 450,000 or more people in Arizona who are here illegally.

 Pearce said rank-and-file police officers want the ability to stop and detain illegal entrants. But he said many have been stymied by formal or informal policies instituted by city officials or police chiefs which block them from routinely inquiring about their status under federal immigration laws.

 Making illegal presence a violation of state law ensures that police have clear authority to make arrests solely on the basis of illegal presence.

 The other half of the legislation is designed to prevent city officials and others from basically directing their officers not to enforce this law.

 It even includes teeth: Individuals who believe state, county or local officials are blocking police from enforcing the law can sue. Judges would be empowered to withhold all state funding “until the policy is rescinded’’ or levy penalties of $5,000 a day.  Tuesday’s vote provoked a sharp debate over how active a role the state and local governments should take in dealing with illegal immigration.

 Rep. Tom Chabin, D-Flagstaff, said legislators should not be telling individual communities what should be the priorities of police. “Some like the way the local sheriff does ‘sweeps’ to capture dishwashers and people who clean our homes and people who work in nursing homes,’’ he said, referring to Maricopa County Sheriff Joe Arpaio. “Law enforcement in local jurisdictions has their own discipline and their own community standards and their own sense of priority of keeping the streets safe and capturing real criminals,’’ he said. “We don’t see the need, then, of this nuisance legislation.’’

 And Rep. Tom Prezelski, D-Tucson, said this kind of law would be “wasting the time of our police departments.’’ Pearce said the measure is not designed to make police into immigration enforcers. He said the measure, if it becomes law, ensures that individual officers have the ability to pursue cases where they believe people are here illegally, even if that is only a decision to call ICE.

 But Rep. Steve Gallardo, D-Phoenix, said nothing in law bars officers from notifying federal officials of suspected illegal entrants. “This takes it a step further,’’ he said. “It gives them a whole ‘nother layer of responsibility,’’ Gallardo continued, one he said which creates more work for police who should be battling crime.

 Rep. John Kavanagh, R-Fountain Hills, countered that police officers are blocked from using their judgment because of local “sanctuary’’ policies which he said tie the hands of officers — policies that would be barred if this measure becomes law. “During the course of a routine patrol, arrest or summons, they should be able to pursue the immigration status of anybody they have reason to believe is here illegally,’’ he said. “If they would do this, we would have plenty of enforcement and we would be removing many dangerous criminals from our streets.’’

 And Kavanagh said if some legislators oppose having the state set the policy, he said they should be similarly opposed to having local elected officials do the same. “Let’s give the local cop on the street the authority to use his instincts and his training to take care of this problem,’’ he said. “Cops know what to do,’’ Kavanagh continued, saying they deal with all types of crime. “Illegal immigration should not be exempt from scrutiny and good-faith efforts of our law enforcement officials to crack down on this problem and all of the resulting economic, social and political problems it causes our state.’’