What is the directive that if a driver unintentionally runs over a person, there is no expiation upon him, whereas if a mother unintentionally rolls over her baby while asleep and kills it, expiation is required of her?

There is no expiation incumbent upon the driver if he accidentally runs over a person without having committed an act that necessitates liability, such as when the accident is a result of a force majeure, the action of the injured party, or the fault of another. However, if the running over was due to his own erroneous action, then expiation is incumbent upon him, and the blood money (diyya) is to be paid by his 'aqila (male agnatic relatives responsible for collective payments).

As for the mother who accidentally rolled over her infant, killing it, blood money is incumbent upon her because the killing resulted from her action.

The difference between the two cases lies in whether or not there was an action from the driver, and in what can be avoided versus what cannot. The aforementioned driver did not commit a direct action, unlike the mother whose rolling over her infant was a direct action from her.