One small thing about the Big Apple is the crime rate — New York is America’s safest big city by a mile, new FBI crime stats show.

New York has the lowest crime rate of the 25 largest cities in the country, Mayor Bloomberg announced yesterday. And of the 261 cities with more than 100,000 residents, New York’s crime rate ranked 246th.

Violent crime plunged 4 percent in New York last year, outpacing the national crime decline of 2.5 percent.

The city’s overall violent-crime decrease in 2008 was led by a 9 percent drop in assaults — a plunge that offset spikes in other categories, including a 5.4 percent increase in murders, a 1.7 percent hike in rapes and a 1.8 percent boost in robberies.

In what’s surely more good news for Bloomberg’s re-election campaign, crime also dropped sharply in the first five months of 2009, according to NYPD data.

Murders led the year’s downward trend, dropping 21.1 percent, the NYPD said.

Rapes, robberies and felony assaults are down, too.

“There have been 43 fewer murders, 1,415 fewer robberies and 491 fewer cars stolen than this same time just a year ago,” Bloomberg said.

“Using innovative policing strategies and a focus on keeping guns out of the hands of criminals, we are continuing to do more with less, in spite of the economic downturn.”

Following New York in the lower crime rates for big cities were San Jose, Los Angeles, San Diego, Las Vegas, Philadelphia, Phoenix, Houston, Dallas and San Antonio.

The story was far grimmer in small-town America in 2008.

Places with fewer than 10,000 residents charted a 5.5 percent rise in murders, a 1.4 percent increase in rape and a 3.9 percent rise in robbery.