MIAMI — Lawyers for a government workers’ union and the American Civil Liberties Union on Wednesday urged a federal judge to declare as unconstitutional Gov. Rick Scott’s order that state employees undergo random drug testing.

At a hearing, the attorneys told U.S. District Judge Ursula Ungaro that a blanket policy covering some 85,000 workers in 18 executive branch agencies violates the Fourth Amendment by subjecting them to an unreasonable search without adequate suspicion that they used drugs. The policy instead should focus on workers in safety-related and law enforcement jobs, they said.

“This is contrary to decades of case law,” said Shalini Argawal of the ACLU’s Florida chapter. “The governor has articulated no special need to test all employees.”

Attorneys for Scott, who issued the order last year, countered that there is adequate statistical evidence in years of national studies about workplace drug use and its dangers to justify the order.

“Drugs are very harmful,” said Jesse Panuccio, the governor’s deputy general counsel. “They create danger, not just if you drive a train.”

Ungaro, however, seemed skeptical of the Republican governor’s position. She quoted three key court rulings that say grounds for random employee drug tests should include such factors as “a surpassing safety interest,” a “grave safety threat” and a “concrete danger.”

“Which exhibits show a surpassing safety interest?” Ungaro asked Panuccio, who responded by citing the statistics.

Ungaro did not indicate when she would issue a ruling. Scott suspended the program in June because of the lawsuit, one of two filed by the ACLU regarding Florida drug-testing programs. The other challenges a Scott-backed state law requiring testing for welfare recipients, which a federal judge in Orlando has blocked temporarily.

Meanwhile, legislation cleared a state House committee Tuesday that would allow — but not require — state agencies to randomly test workers every three months. The bill would make it easier to fire those who test positive for drugs.

The ACLU and the workers union, the American Federation of State, County and Municipal Employees, questioned at Wednesday’s hearing whether there was a true need for the blanket testing policy.

They said that in 2010, only 46 of the 85,000 workers in question were subjected to drug testing because of suspicion they were using drugs — about five one-hundredths of 1 percent. Most were in the Corrections and Juvenile Justice departments, and most were found to be drug-free. In 2009, only four of more than 4,700 workers tested were found positive for drugs.

To the governor’s office, however, the solution is simple: People who don’t want to undergo drug tests do not have to be state workers.

“State agencies are not forcing anyone to submit to a drug test,” the governor’s lawyers said in court papers. “Job applicants are free to walk away from the job offer, and employees are free to find other employment.”