"This is a violation of both the mother and child's rights," she wrote in the petition.
The island of 4 million people reported a record 1,117 homicides in 2011, although the majority of crime is linked to drug-trafficking.
The boy's Syrian father could not be reached for comment. Rahim's relatives did not return calls for comment, nor did her attorney.
Rahim, who lives in Puerto Rico with her Palestinian father and Syrian mother, has said she wants custody of her son because the boy's father is a strict Muslim and plans to take the boy back to the war-torn country.
The couple began fighting over the boy in 2010 in a battle that has involved both local and U.S. courts.
Joining the battle now are thousands of supporters and a few dozen detractors, the majority of whom say that Rahim would not be in this situation if she had turned over her son to his father.
Rahim is an instructional designer at Caribbean University, a private school in Puerto Rico's northern city of Bayamon.