The father suffered injuries after punching a car window and getting dragged by the vehicle.
The police were alerted to the accident at 5.07am.
The suspect was conveyed to the hospital before his arrest.
A threatening note filled with vulgarities was also left behind.
The SCDF said two people were conveyed to Khoo Teck Puat Hospital.
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He was reportedly frustrated with her as she refused his offer to take her home.
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Netizens were divided over who was at fault for the incident.
Mountainous areas in the north like Chiang Mai may see temperatures range from 3°C to 10°C.