It was a crime that once would have attracted little attention in Tokyo’s lurid undertow: police are this week hunting a man who used his smartphone to film under a woman’s skirt. The suspect fled across the tracks of Ikebukuro Station after the woman cried for help.

Women subjected to sexual assault on Tokyo’s crowded transport system were once as likely to ignore it: Chikan (groping) was not widely dealt with as a crime until the mid-1990s. Now the police spend considerable energy trying to catch offenders.

One reason is that the police have more time. Crime rates have been falling for 14 years. In the last six months of 2017 they set a new low after falling the previous year below the one million mark for the first time since the second World War.

The murder rate of 0.3 per 100,000 people is among the lowest in the world, and roughly half Ireland’s rate. (In America, where violent crime is rising at its fastest pace since the 1970s, it is more than 5). Gun-deaths rarely rise above 10 a year.

Virtually the one rising criminal fraternity is the elderly. Senior citizens now account for about 20 per cent of arrests and detentions. As the population ages the over 65s commit nearly four times more crimes than they did two decades ago.

One result is that Japan’s jails are filling up with the infirm: more inmates need help with walking, bathing and even using the toilet. The government recently allocated a budget to send care workers to about half of the nation’s prisons.

Yet, Japan has more than 15,000 more police personnel than it had a decade ago, when crime rates were far higher. The density of officers per population is particularly marked in Tokyo, home to the world’s biggest metropolitan police force.

Forensic rigour

In practice, this means lots of police attention. Petty drugs offences are treated with forensic rigour. Police have arrested athletes, rock stars and university students for smoking pot. One woman recalls five officers crowding into her cramped apartment after she reported her knickers being swiped from a clothesline.

As they run out of things to do, however, police are becoming more inventive about what constitutes a crime, says Kanako Takayama, a professor of criminal law at Kyoto University. In one recent case, she says, they arrested a group of people who had shared the fees for a rented car because they judged it was an illegal taxi.

Critics who fret about over-enthusiastic police cite a week-long stakeout in 2016, in Kyushu, southwest Japan. Five officers watched over a case of beer in an unlocked car outside a supermarket in Kagoshima, scene of a series of car robberies, before pouncing on the hapless middle-aged man who eventually helped himself.

A judge dismissed the case, which he called an unnecessary and expensive sting operation.

In another incident reported by the liberal Asahi newspaper, police in rural Gifu Prefecture spied on local citizens who opposed a wind power project, then repeatedly called executives from the power company in 2013 and 2014 with detailed reports on the activists, including ages, academic background and medical records.

Oddly, the police increasingly struggle to solve crimes. The rate of detection for total offences fell to a post-war low of less than 30 per cent in 2013, which suggests that while crimes happen increasingly rarely, the police are not very good at solving them.

The latest annual White Paper published by the National Police Agency cites weakening community ties as well as widespread use of mobile phones, the internet and other technological advances as factors for falling detection rates.

People police themselves

Confessions, often made under duress, form the basis of nearly 90 per cent of criminal prosecutions. The reason why Japan looks so good is that people police themselves, says Yoshihiro Yasuda, a campaigning lawyer.

Japan’s justice system gets a lot right. Rates of recidivism (reoffending) are low and much effort is made to keep young offenders out of prison. Adults are incarcerated at a far lower rate than in most developed countries – 45 per 100,000 compared with 666 the United States.

Precisely because it is so safe, however, some fear the system is ripe for abuse. With little else to do, police may start finding new things to enforce, says Colin Jones, a legal expert at Doshisha University.

In 2015, a man was arrested for scribbling Adolf Hitler moustaches on to posters of prime minister Shinzo Abe. Leaked internal police documents in 2010 described intensive surveillance of Tokyo’s largely trouble-free Muslim community. A “mosque squad” made up of dozens of officers monitored Muslims and cultivated informants.

Last year the government gave the police even more powers with a new “conspiracy” law that allows them to investigate and arrest people who plan to commit crimes.

Whereas in some parts of the world, you can never find a cop when you need one, Japan may have too many.