A man and woman in their 20s have been arrested after police say they found them in "an extremely incoherent state" with a small child in their car.
The incident is reported to have taken place on Hillhead Road, Toome on Sunday night.
Front bumper and wheel damage was also discovered on the vehicle.
It is understood arrangements were made to care for the child after the pair were taken into custody.
A Mid Ulster PSNI spokesperson posted on their Facebook in the early hours of Monday: "Crews stopped with this vehicle tonight on the Hillhead Road near Toome.
"The car had front bumper and wheel damage. We found two adults in the vehicle, both were in an extremely incoherent state and struggled to maintain focus and conversation with the officers, both believed they were driving.
"The two have been arrested. A small child also in the car was removed from it and looked after by crews.
"Arrangements have now been made for the child to be cared for."
A police spokesperson later added: "Police in Antrim came across a vehicle parked on the A6 bypass at Toome at around 9.15 pm on Sunday, April 5.
"A 29 year old woman was arrested on suspicion of driving when unfit, in charge when unfit and possession of a class C controlled drug.
"A 29 year old man was arrested on suspicion of driving when unfit and in charge when unfit through drink or drugs.
"They both remain in custody at this stage."
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