( CNN ) -- High levels of illegal immigration and crimes committed by unauthorized immigrants are among the key rationales cited by some supporters of a tough new immigration law in Arizona . `` Border violence and crime due to illegal immigration are critically important issues to the people of our state , '' Arizona Gov . Jan Brewer said at the signing of the controversial bill , SB 1070 . `` There is no higher priority than protecting the citizens of Arizona . We can not sacrifice our safety to the murderous greed of the drug cartels . We can not stand idly by as drop houses , kidnappings and violence compromise our quality of life . '' Yet , a look at statistics from the U.S. Customs and Border Protection agency and the FBI indicate that both the number of illegal crossers and violent crime in general have actually decreased in the past several years . According to FBI statistics , violent crimes reported in Arizona dropped by nearly 1,500 reported incidents between 2005 and 2008 . Reported property crimes also fell , from about 287,000 reported incidents to 279,000 in the same period . These decreases are accentuated by the fact that Arizona 's population grew by 600,000 between 2005 and 2008 . According to the nonpartisan Immigration Policy Institute , proponents of the bill `` overlook two salient points : Crime rates have already been falling in Arizona for years despite the presence of unauthorized immigrants , and a century 's worth of research has demonstrated that immigrants are less likely to commit crimes or be behind bars than the native-born . '' Backers of the bill maintain that crime is a key reason for the necessity of the tough immigration law . Arizona state Sen. Russell Pearce this week told CNN 's Tony Harris that half the murders in Phoenix are committed by unauthorized immigrants and that the city is the second in the world in kidnappings . A CNN Fact Check found that the senator 's claim about the murders in Phoenix can not be proven , but he did have police statistics to back up his claims of the city 's high number of kidnappings , although its exact standing in the world is not clear . In Maricopa County , which includes Phoenix , Sheriff Joe Arpaio has long been an advocate of tough measures against illegal immigration . His officers already check the immigration status of people they detain for other crimes , he said . `` We 've been doing it for a long time , but this [ law ] gives us just a little more authority , '' Arpaio told CNN . One way that Arpaio says he measures his success is that he hears that immigrants who entered the country illegally are leaving his county . `` It 's a good indicator , '' he said . Statewide illegal immigration trends are harder to gauge . One aspect of it is the number of apprehensions of unauthorized immigrants made by the U.S. Customs and Border Protection agency . Since a peak in 2000 of more than 600,000 illegal crossers apprehended , the number fell to 241,000 in 2009 , Tucson Sector Public Affairs Officer Mario Escalante told CNN . `` We 've seen a steady decline , '' he said . Intelligence-driven operations have increased the effectiveness of the Border Patrol 's efforts , he added . Meanwhile , the cartel violence that has gripped Mexico for the most part has remained there , he said . Human and drug smugglers are being `` more aggressive because we 're being successful , '' Escalante said , `` But we 've been lucky not to see that type of [ violence ] spill over here . ''
FBI statistics : Violent crimes reported declined by nearly 1,500 over four years . Comment: CNN Fact Check : Kidnapping is up in Phoenix , but murderers ' status ca n't be proven . Arizona immigration trends murky , largely due to declining border apprehensions .