"Following this his residential premises was subsequently searched," they said.

Mr Speirs was granted bail and will face court at a later date.

The police statement followed Mr Speirs' post on social media announced he would formally step down as the member for Black, in Adelaide's south, when parliament resumed on October 15.

"Since allegations of illicit substance use in my home became public, my home has been raided by armed police, I was arrested and I was questioned," he said in a video.

Mr Speirs said he did not believe he could "adequately and effectively serve my local community while also dealing with this matter, protecting my mental health and supporting my family and friends".

He said he would suspend his Liberal Party membership and thanked his colleagues for their support.

"For me it's time to move on, I want to rebuild myself over the coming months and into the future," Mr Speirs said.

"I want to be a better son, I want to be a better friend, to be honest, I want to be a better person.

"That takes time, and I believe it's best done away from public life."

Mr Speirs resigned as opposition leader on August 8 and was replaced by Vincent Tarzia, who said on Saturday the party's state executive had ratified the suspension of Mr Speirs' membership.

The party respected Mr Speirs' decision to quit, Mr Tarzia told reporters.

"It's obviously a very hard, challenging decision for him," he said.

"I know he hasn't made that decision lightly."

Standing down was in the interests of Mr Speirs own mental health and welfare, "but also in the interests of his community and the parliament", Mr Tarzia said.

He said the party now focused on preselecting "the best candidate we can" to hold the seat of Black, which Mr Speirs has held since 2018.

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