For filicidal research postpartum depression is typically discounted as a contributing factor at the 6-12 month mark (depending on the study), however, depression is prevalent in roughly 70% of all filicides according to some research that has been conducted and women are more likely to develop mental illness during the postpartum period than at any other time.
Psychotic maternal filicides account for less than half of all maternal filicides though, in my opinion, extrapolating data from studies. Many women who kill their children are mentally ill but still clearly able to differentiate between right and wrong; e.g. depression, personality, anxiety and mood disorders.
Susan Smith, Diane Downs, Darlie Routier and Casey Anthony are all examples of mentally ill but not psychotic women who committed non-psychotic filicides. Dena Schlosser and Andrea Yates are very classic examples of psychotic filicides.
Typically in cases of psychotic filicide a confession, or sometimes a suicide attempt, is almost instantaneous. I cannot personally recall a psychotic filicide occurring in which the parent lied to authorities or attempted to conceal their involvement, the child's whereabouts or the nature of the crime. FWIW and JMO