Pol Maj Suriyan Chansai, an investigator at Doi Saket station, said Patchuda Jayruan, 23, appeared intoxicated when she was rescued from her overturned black Toyota.
The woman was later found to have an alcohol level of 67 milligrammes per 100 millilitres of blood, well beyond the legal limit of 50mg per 100ml.
After she recovers Ms Patchuda will be summoned to acknowledge a charge of causing deaths by drink-driving, Pol Maj Suriyan said.
Ms Patchuda told investigators she was returning to her home in Doi Saket district after leaving a party in Muang district, the officer said.
She told officers that before the accident she had taken a brief nap on the side of the road and admitted to drinking alcohol before driving, Pol Maj Suriyan said.
Ms Patchuda was injured in the crash and admitted to Lanna Hospital in Muang district.
Police were alerted to the crash at 6.15am around kilometre marker No.8 on Highway 118 of the Chiang Mai-Chiang Rai road.
The three cyclists killed were Saman Kantha, 62, Chaiwat Yonglan, 63, both from Chiang Mai, and Pongthep Khamkaew, 40, from Chiang Rai.
Two of the injured cyclists were Pongsak Polsing, 36, and Supol Tasing, 56, both from Chiang Mai. Four others sustained minor injuries.
Mr Pongsak, who suffered leg and back injuries, said 20 cyclists from the Sua San Sai cycling club had planned to cycle from San Sai district of Chaing Mai to the Maekajarn Hotspring in Wiang Pa Pao district of Chiang Rai.
They split into three groups and started cycling before dawn.
A car travelling at high speed and swaying from side to side moved past the last group and hit the second group of five cyclists, Mr Pongsak said.
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