The man, Joshua James Baker, 32, whose passport lists his place of birth as Mt Isa in Queensland, is now in police custody but is yet to be officially declared a suspect.
It comes after he allegedly escaped from police custody on Monday and spent 10 hours on the run before he was rearrested.
A police source told News Corporation that the man was taken to a police hospital after complaining of feeling ill. When he asked to go to the toilet it is alleged he then escaped. He was arrested later in the day at a Kuta hotel.
Customs officers say that the drugs were allegedly found after officials became suspicious of the man’s luggage when it was X-rayed.
Baker had arrived in Bali on a flight from Thailand on Sunday afternoon and was handed from the Customs authority to police on Monday.
Ngurah Rai Customs and Excise chief Budi Harjanto said his officers found 36 grams of marijuana mixed with tobacco in Baker’s luggage along with 37 Diazepam antidepressant pills.
“He went through the Customs like other passengers. We felt suspicious when his luggage passed through the custom’s X-Ray. When we checked, we found the drugs inside his bag,” Mr Harjanto told News Corporation.
He said the drugs had tested positive to marijuana using a rapid narcotic test.
“Yes, its positive to marijuana. We have done a test using our rapid narcotic test,” he said.
“He said he brought it only for individual use, for himself. He said the drugs were planned to be used by himself. But we don’t know the truth,” Mr Harjanto said.
He said Baker had told officials he was in Bali for a holiday.
Deputy Director of the Narcotic Directorate of Bali Police, Suwardjoko, said police were still forensically testing the pills to see if they were definitely Diazepam.
“The Australian was coming for a holiday, but he brought pills. It’s like an anti depressant pill. but we are still investigating. We will check it in the laboratory, is it true it is a sedative,” Suwardjoko said.
He said police were yet to interrogate Baker fully about the case.
“He said that it is an antidepressant. He said he is sick, that he got depression, so he needs the medicine,” he said.
“We haven’t conducted intensive interrogation of him. We will check it in the lab first, after that, we will conduct intensive interrogation.”
Indonesia has harsh anti-drugs laws which punish offenders with jail terms for even small amounts of drugs.