* Criminal network believed to have corrupted politicians
* "Capital mafia" operated to win public contracts
* Case follows scandals in Milan, Venice city governments
By James Mackenzie
ROME, Dec 4 (Reuters) - The mayor of Rome ordered a review of city contracts on Thursday after a police investigation revealed a web of corrupt relationships between politicians and criminals in the Italian capital.
Police arrested 37 people and placed dozens more under investigation on Tuesday in the latest scandal to hit Italy, ranked one of the most corrupt countries in Europe in Transparency International's latest global corruption index.
So far, the case has not hurt Prime Minister Matteo Renzi, who said he was "shocked" by the revelations.
But after scandals this year with the 2015 Milan Expo and the Venice flood barrier corporation , the arrests have underlined how far graft runs in city administrations across Italy.
The former mayor of Rome, Gianni Alemanno, is among those under investigation. He denies any wrongdoing but has resigned from his position in the right-wing Brothers of Italy-National Alliance party.
Alemanno, who began his career in the party which succeeded the old Fascist party of Benito Mussolini, is the highest-profile politician implicated in the new scandal.
Figures on the right have been most in focus but members of Renzi's Democratic Party (PD) have also been accused. Several officials in the current centre-left administration of mayor Ignazio Marino have resigned, though they too deny wrongdoing.
Facing calls from the opposition 5-Star Movement for his administration to quit, Marino said he had asked the National Anti-Corruption Authority to investigate a list of potentially suspect contracts.
Renzi also ordered the local Rome PD branch to be put under special supervision by the party's national chairman.
Prosecution documents include transcripts that show how unscrupulous entrepreneurs captured lucrative public contracts, often profiting from serious social problems in a city long close to bankruptcy.
"Have you got any idea how much you can make out of immigrants?" says one, referring to subsidies for providing services at temporary camps for Roma and other migrants. "Drug trafficking brings in less".
Police have classified the case as a mafia investigation because it was organised like a mob clan. However, they say it is not connected to southern Italian mafias such as the Sicilian Cosa Nostra, the Naples Camorra or the Calabrian 'Ndrangheta.
They believe the network, dubbed "Capital Mafia", springs from violent neo-fascist formations active in the 1970s and '80s and a notorious Rome criminal group of the time known as the "Magliana Gang". (Editing by Gareth Jones)
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