The truth of this is a few points.
1 - Cops get their revenue more by fines through finding crimes to keep their numbers up during cutbacks. They have to get their money somehow and the citizens are the easiest victims to roll for it.
2 - More cops find more crimes - In Akron, Ohio the more cops on the street find excuses to pull people over and look for a secondary reason to be able to bust whoever. The amount of drug-busts in Akron during Quota week are entertaining as the cops pretty much walk along a few streets and just pick up the more obvious drug addicts and find an excuse to bring them in to put thme into the rehab station that is close to the University, perpetuatiing a vicious cycle.
3 - More laws that allow cops to harass citizens in many ways without fear of reprisal or consequences for this harassment leads to a dangerous mentality. This has been proven time and again by history and needs few examples past The Secret Police of any large Regime. Tighter laws along ith making it easier to arrest more it also would allow
4 - Hard times under Republican regimes have caused an increase of crime due to a lack of ability to pay bills, rent or much of anything. Nobody can live by themselves on 10 bucks an hour, even at 40 hours a week. Especially after taxes and everything else are taken out. Right now the minimum wage is... 5.35 an hour? Oh my, I see a bit of a problem there. I wonder if it's related to the doubling of food stamps, medicaid and other government subsidies in towns where Wal-Mart takes up residence too? When people are desperate crime goes up with unrest.
5 - Trickle-down Economics - This is a hugely popular Republican mythological financial scheme. Somehow this myth turns up in the Republican controlled administrations where the basic idea is that they'll give so much money to the people who already hoard.... and save... and have a lot of money... and that they'll have so much more they'll just piss out extra waste money that will bring the poor people up in class. It is a modified theory from feudal times known as Surfdom, it failed too for the same reason trickle-down economics, golden shower economics as it should be named, just doesn't work for econimic mobility and has not. Of course, one must also note that generally people get upset when someone is urinating upon them.
6 - Rep-race Reactionism - For some reason Republicans are really great about saying they aren't racist but they have a lousy track record for acting like they are. From comments from the First Mother that do not bear repeating any more than Let them eat cake. To the more recently fired Islamic Fascist salvo or Muh-kah-kah (SP?) grenade dropped in front of a video camera. To me it is only comparable to watching an autistic child try to comprehend some social nuances then getting frustrated and throwing a fit. Historially this has lead to an increase of crimes in racial areas, both surrepticiously and hate-crime driven.
7 - In Corp we trust? - It seems as though the Republican Regimines, though almost all politicians to come extent, are hot and heavy with business interests. Corporate interests comming before the interest of the people. Often it seems as though people become commoditized in a pattern that has lead to the death of liberties and truth with the birthchildren being secrecy and conspiracies. Under Regan the News was subtly set loose to allow it to be partisian, It took some time before the Republican Machine moved in it's taling heads. Rush Limbaugh and other corporatized cheerleaders feed misinformation without having to support it with annoying facts or evidence. This then affect those on the bottom of the scale who are vilianized for being lazy, dumb, lacking initiative and more.
THere are many many more reasons as well, but these are some of the main macroreasons with simplified explanations of why the REpublican Regimes cause increases in crime.