The accused, Mariyamma, visited the branch at Kondotty yesterday to deposit Rs 49,500 of which bank officials found currency notes with a face value of Rs 37,000 to be fake.
All the notes were of Rs 1000 denomination.
SBI officials immediately informed police.
When questioned, the woman had stated that her children who were in the Gulf had sent her the money, police said.
A case has been registered under IPC section 489 (B)(C) (using as genuine, forged or counterfeit currency or bank notes, possession of forged or counterfeit currency or bank notes), they added.