He argued there was no medical evidence to support that charge.
McKean said in her second police interview, the mother said her husband choked the baby and squeezed him till he turned purple.
In the third police interview, she admitted making up the choking bit by her husband.
"The court cannot, on the basis of that evidence, rule there is a case to answer," McKean said.
In response, Crown solicitor Mike Smith accepted there was no direct medical evidence to support the charge but the evidence required to convict her was contained in her statements to police.
She resiled from choking but not from impeding the breathing of her baby, he said.
Justice Gerard van Bohemen will deliver his ruling on McKean's application on Monday.
McKean will inform the court on Monday whether the defence will either call or give evidence.
Earlier, a St John paramedic gave evidence and said the baby was not breathing, was floppy, wet, and cold when she picked him up from the shower floor.
The paramedic started chest compression with her fingers, given the age of the baby, and did rhythm checks for about 30 minutes before pronouncing the child dead.