Beasley was arrested early Tuesday following a traffic stop, according to Officer David Pubins.
An officer found three cigarettes suspected to contain marijuana in Beasley's Mercedes after smelling marijuana during the stop, Pubins said.
Beasley was released after being cited for investigation of one felony count each of marijuana possession and possession of drug paraphernalia.
According to Pubins, court proceedings in the case will begin once results of lab tests are available.
Beasley, the No. 2 overall pick in the draft by Miami out of Kansas State in 2008, signed a three-year, $18 million contract with the Suns a year ago. But he went on to have a disappointing, inconsistent season, averaging career lows of 10.1 points and 3.8 rebounds in 75 games as Phoenix compiled the worst record in the Western Conference and second-worst in franchise history. He shot 40.5 percent from the field, also a career worst.
Marijuana issues followed Beasley to Arizona.
In June 2011, Beasley was ticketed for possessing marijuana and speeding in a Minneapolis suburb. He also has acknowledged that while playing for Miami, he twice violated the NBA's drug policy and entered a treatment facility in 2009.
At a news conference following his signing with the Suns, Beasley pointedly said he was through with marijuana.
"I realize 10 minutes of feeling good is not really worth putting my life and my career and my legacy in jeopardy," he said then, "so I'm confident to say that that part of my career, that part of my life, is over and won't be coming back."
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