Suzanne Buchanan, also a British national and who was named in the warrant, is accused of publishing false information on the website, thus tarnishing the reputation of Koh Tao and violating the the computer crime law.
The offence carries a maximum jail term of five years and a fine of B100,000, the source said.
The police have also threatened to press charges against the moderators of popular Facebook pages who spread "false" information in addition to 20 others who shared it online.
Immigration police yesterday searched two locations on Koh Samui in the hunt for Ms Buchanan. However, they found no trace of her, the same source said.
In July last year, a group of people on Koh Tao filed a complaint against Ms Buchanan after the website published a story about the death of a Belgian tourist and claimed she was murdered.
Surat Thani Police Commander Maj Gen Apichart Boonsriroj yesterday submitted a report to Provincial Police Region 8 Commissioner Pol Lt Gen Sorasak Yenprem.
Gen Apichart said their investigations revealed that the alleged rape did not take place as claimed by the British tourist. However, he said police will launch a fresh investigation if new evidence surfaces.
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