They have said it may take up to six weeks before they decide whether to lay charges over the death.
"Police require further medical evidence," Mr Lawson said.
"The investigation is ongoing. It may or may not result in further charges depending on the outcome."
Judge Arthur Tompkins bailed Pene until July 18.
Outside the courthouse the family, most understood to have travelled down from Kaitaia, refused to speak about the incident but slammed the media coverage.
Trent had been living with his uncle Joe Matthews and his partner, Pene, since birth. The pair have two other boys, Chavawn, 7, and Joby, 1. Trent was the son of Joe's sister Tania.
Pene's brother, speaking from Ahipara in the Far North, told the Herald the family stood by her and didn't think she would do anything to hurt a child.
"She's a good mother, she's not that sort of person."
Pene has described herself as a "family kinda gal" on the social networking site Bebo and says she has a "beautiful son" and a "lovely fiance".
Rotorua residents upset by the tragedy have driven past the Edmund Rd house Trent died in, several placing teddy bears and toys by the letter-box in memory of the child.
A neighbour, who did not want to be named, said the family had not returned to their home since the police investigation began. Friends had visited the house on the night of the tangi to mow the lawns, collect mail and move the toys on to the front step under shelter from the rain.
