They said Jenishah (28) had given poison to her daughter Selin Pupsia (6) and four-year-old son Sujith by mixing it in sweets and then consumed it herself last night.
Her husband Justin, who returned around midnight found them unconscious and raised an alarm. Neighbours rushed all three to a hospital, where doctors declared the woman and child brought dead.
Selin's condition is stated to be serious.
Police said Jennishah was worried about a housing loan and her own physical illness and had told her relatives about her problems.