As police searched for a missing baby, parents Calvin Melvin and Brittney Sierra each told investigators their own theories:

If the baby is dead, “Melvin did it,’’ Sierra said, according to documents released this week by the Broward State Attorney’s Office. When asked by detectives how her long-time boyfriend would have killed the child, Sierra said Melvin would have taken the blue pillow from the stroller and suffocated their son.

But Melvin, the child’s father, said if anything had happened to Dontrell, it was Sierra who had harmed him. Then, for good measure, he drew a diagram of the backyard of the Hallandale Beach home they had rented when the child disappeared, showing police where the baby would be buried if Sierra had killed him.

He then suggested police look under the ground behind the house because “Sierra is always home with the kids and always by the back yard.”

That’s exactly where in January authorities discovered the tiny remains presumed to be Dontrell Melvin, who was last seen in July 2011 when he was 5 months old.

He wasn’t reported missing for 18 months, when a Department of Children and Families caseworker went to the home Sierra shared with her mother and half-siblings.

Calls had come into DCF that Sierra was taking drugs and using profanity, according to documents.

“The mother is smoking marijuana mixed with an unknown drug in front of the children,” the tipster said. “Mom verbally abuses the children.”

Sierra, 21, has been charged with two felony counts of child neglect and Melvin, 27, has been charged with three felony counts of providing false information to police. The couple could face more charges if the bones are indeed Dontrell’s.

Police are awaiting DNA confirmation from a Texas lab that the femur found buried in the backyard at 106 NW First Ave. belonged to Dontrell, who would have turned 2 in February.

As soon as a DCF case worker reported the child missing on Jan. 9, police began piecing together stories from Sierra, Melvin and Melvin’s family members.

According to the 37-page State Attorney’s Office file, which includes a detailed timeline and statements from detectives who interrogated the couple, Sierra stuck to the same story:

The last time she saw Dontrell, her boyfriend was pushing him in his stroller northbound on Northwest First Avenue from their home. Calvin told her “he was going to walk to the store to get some smokes and he was taking Dontrell with him.”

Sierra said she went for a shower and an hour later Melvin came back without the baby.

He told her he’d run into his mother, Annie Melvin, and given the baby to her because he and Sierra were having financial difficulties.

Sierra told police she begged to visit her baby, but Melvin always had an excuse.

Three times she called Annie Melvin’s home to ask about Dontrell, and each time she was told the child wasn’t there, according to the State Attorney’s Office documents.

What would have been the baby’s first Thanksgiving passed. She signed Dontrell up for a charity Christmas gift program, indicating the child would be 9 1/2 months old, but she didn’t see him over Christmas or even for his first birthday. More holidays passed without seeing her child.

“Based on the arguments, Sierra accepted that Dontrell was OK with Melvin’s family and moved on day after day without Dontrell in her life,” Hallandale Beach detectives wrote.