The 27-year-old man is being questioned about an assault on a female member of staff at the Co-op in Broadway, Hawksworth.
Police today said that the woman had needed stitches to her face after a man hit her with a bottle shortly after 7.20am.
Officers now believe the person responsible may also be linked to a separate assault and a crash, both of which took place yesterday morning.
A spokesman said they had been called to reports of a disturbance at Regents Close in Horsforth at around 6.30am.
He said a 38-year-old man had been taken to Leeds General Infirmary with a serious hand injury.
Reports of a collision were then received at 7.15am after a Volkswagen Golf and a Toyota crashed in Abbey Road, Kirkstall.
The spokesman said the three incidents were being treated as linked following enquiries.
He said the 27-year-old was arrested later on suspicion of two counts of assaults and one of dangerous driving.
The man remains in police custody this afternoon.