The couple will remain in custody until the ruling is made.
One of the girls, who can only be identified by her first initial "M," died last month after a judge ordered she be removed from life support.
The girl's parents currently face two counts each of aggravated assault, criminal negligence causing bodily harm and failing to provide the necessities of life.
Crown prosecutor Shelley Bykewich said Thursday no decision has yet been made on whether the charges will be upgraded.
The man and his wife, who are not allowed to communicate with one another, sat in separate prisoner boxes in a packed Court of Queen's Bench courtroom.
It's their first time in court following a brief but intense legal battle in which the couple sought to keep "M" on life support over the advice of doctors, who testified the girl's brain damage was so severe that she would never regain consciousness.
The parents argued that taking the girl off life-support was against their religious beliefs.
Health-law experts said the case may have wide-ranging effects on future cases, setting a precedent where taking someone off life-support could be in their best interest.
The couple has been in custody since June when paramedics, on a call to the family's south Edmonton home, discovered the twin girls severely malnourished.
One girl weighed 13 pounds and her sister 16 pounds. Police said girls that age should weigh around 26 pounds. The girls' older brother was found in good health.
The parents cannot be named under Alberta law because the surviving children are now wards of the province.
Justice Terry Clackson will deliver his decision on bail within the next 21 days.
A date for a preliminary hearing was also set Thursday for June 2013.
If the matter is ordered to go to trial, the case would not be back in court until the following year.