Willie Nelson’s famous habit of smoking marijuana is not seen as a badge of outlaw courage here anymore, so much as the frivolous foible of an eccentric uncle. A popular FM station disgorging the Boomer rock hits of yesteryear calls itself Hippie Radio 94.5; one of its sponsors is a smoke shop that incessantly hawks glass pipes and detox kits. Even mainstream country acts mention smoking marijuana now and again among the litany of acceptable American pastimes.

So perhaps it is not surprising as much as telling that this city, which residents often refer to as the Buckle of the Bible Belt, may be on the cusp of joining the long roster of American cities, including New York, that have decriminalized the stuff.

On Tuesday, the Metropolitan Council, the legislative body for the consolidated city-county government here, will vote on a proposed ordinance that would give the police an alternative to criminally charging people caught with a half-ounce of marijuana or less.

Under the ordinance, officers will have the discretion to forgo a misdemeanor charge for marijuana possession, and instead issue a civil citation with a $50 fine. A judge could then suspend the civil penalty if the person cited agrees to perform up to 10 hours of community service. The goal here, as elsewhere, is to keep minor drug offenders from clogging the court system, and relieving them of the stigma of a record.

It is hardly a sweeping measure, and hardly the most significant American drug policy reform under consideration this year: In November, voters in five states, including California, will consider legalizing recreational marijuana, while at least three states, including Florida and Arkansas, will decide whether to legalize its medical use.

But the fact that the decriminalization proposal has a good chance of passing here in Nashville — the great promulgator of heartland values in song, and home to the conservative Southern Baptist Convention — says something about the steady erosion of the fear of marijuana, which, for many here, has come to seem about as threatening as a Lady Antebellum ballad.

The fear in Nashville was palpable once. In October 1980, the city’s police chief, Joe Casey, declared in a front-page article in The Tennessean that marijuana caused people to rob and kill. Anyone caught growing or selling marijuana three times, Mr. Casey said, or selling it to minors once, should be executed.

Asked at the time if it should be legalized, Mr. Casey replied, “God forbid.”

Today, the sheriff of Davidson County, Daron Hall, has called the proposed decriminalization ordinance a “step in the right direction” to reduce incarceration rates. The current police chief, Steve Anderson, said he was “neutral” on the bill. Sean Braisted, a spokesman for Mayor Megan Barry, one of the South’s most liberal big-city mayors, said that Ms. Barry had not taken a position on the ordinance, though “generally she’s supportive of the idea of decriminalizing marijuana.”

A sponsor of the proposal, Councilman Russ Pulley, is a former police officer and state trooper and retired F.B.I. agent, who chuckled when asked if he smoked marijuana himself. (He does not.) He is among many lawmakers around the country who believe that criminal justice resources should be reserved for more serious matters, and worry that criminal drug charges on the records of young people may prevent them from finding good jobs.

“These kids that have made stupid mistakes — I hate to see them carry these stupid mistakes with them the rest of their lives,” Mr. Pulley said.

Others, including the American Civil Liberties Union of Tennessee, have urged council members to approve the bill, arguing that black residents have been disproportionately arrested on charges of possession of small amounts of marijuana.

The proposal comes as mainstream country music, the city’s signature cultural export, has experienced an apparent uptick in mentions of pot usein recent years. “Walkin’ to the south out of Roanoke,” Darius Rucker sang in his hit “Wagon Wheel,” which went to No. 1 in 2013 on Billboard’s Hot Country Songs chart. “I caught a trucker out of Philly had a nice long toke.”

For Todd Snider, a singer-songwriter here with roots in country’s less commercial folk, outlaw and Americana strains — where songs about drug use have long been common — the occasional mention of marijuana smoking in mainstream country says something about where the middle of the country stands.

“That’s the barometer,” he said of the mainstream country charts. “Those guys don’t say stuff that mom don’t tolerate. And mom’s like, ‘Ah, pot’s not so bad anymore.’”

Doak Patton, a Nashville native and president of the Tennessee chapter of Norml, the National Organization for the Reform of Marijuana Laws, agreed. “It’s not a big deal anymore,” he said. “There used to be a terrible stigma associated with it. I think that’s gone.”

But Mr. Patton, a former criminal prosecutor, said that almost no one from the country music community had lent their support to his group. He opined that some conservative fans might still view such activism as inappropriate. “Agents just think it’s the kiss of death here,” he added. “People are not as open as they are in Oakland.”

Nashville, of course, is as much a city of health care executives as it is country stars, and Mr. Patton said that his other supporters represent a wide swath of everyday Nashvillians, including people interested in marijuana’s medical applications. Mr. Pulley, the co-sponsor, said that a number of people in the music industry have contacted him and told them they supported the idea.

The opposition so far has been scant. On Friday, a representative for the Southern Baptist Convention declined to comment on the proposal. The critics include State Representative William Lamberth, a Republican, who argues that the proposal amounts to Nashville “pretending to decriminalize” marijuana. If it passes, he said, police officers could play favorites, giving a civil citation to people whom they like, but slapping those they don’t with a misdemeanor.

“My real worry is that they pass this ordinance, and all these people in Nashville, and people who are visiting Nashville, think that it’s legal,” he said.

But for Mr. Snider, who lives outside the city limits but still plays, records and socializes in the city, the proposal seems like a move in the right direction, especially for a city with a world-famous creative-class economy.

On Thursday night, Mr. Snider, whose music straddles the line between country, folk and rock, sat in his living room with a fat green bag of marijuana on a table, occasionally packing it into a pipe and puffing as he spoke of the life of a songwriter.

He described a good song as something to be caught, as if it were butterfly. Marijuana, he said, afforded people like him a wider net. It was, he said, an essential tool of Nashville’s signature trade.

“For starters, our job is to lower our inhibitions,” he said. “And anyway, if Paul McCartney does it, you’d be a fool not to do it.”

Original Article via NYTimes