They were declined electronic bail when they appeared before Judge Michelle Howard-Sager.
Both are due back in court on March 23 for another bail hearing.
Brown-Martin will appear in person but it is not yet clear if that will be the case for Witehira, who is believed to be in Auckland Women's Prison at Wiri.
Police were alerted to the alleged kidnapping by bank staff. Witehira was arrested shortly afterwards when police boxed in her Audi on Williams Rd in central Paihia.
About an hour later Brown-Martin crashed into a fence at the Affco freezing works in Moerewa. He suffered serious injuries and was flown to hospital in Whangārei, where he was placed under guard.
He was not being chased by police at the time.