Attorneys representing 37 immigrants who are being kept at the Chaguaramas Heliport are expected to write to regional and government officials seeking permission for them to stay in TT pending guidance from regional bodies.
The migrants which consists of 20 children and 17 adults were found aboard a vessel approaching TT's south coast on Saturday night.
A media release from the coast guard reported that sailors attempting to stop the boat from escaping shot at their engines.
This led to the death of one-year-old Ya Elvis Santoyo and his mother being wounded.
Speaking with Newsday on Wednesday attorney Criston J Williams said he and colleagues received instructions from the migrants to write to National Security Minister Fitzgerald Hinds seeking his permission in having them stay in TT.
"These correspondences will be to the Minister of National Security for granting the people on the boat asking them for the minister's permit in accordance with Section 10 of the Immigration Act as well as the Immigration Manual to have a minister's permit to stay in the country.
"We're also writing the UNHCR to help with a determination of their status as well as we're also seeking the assistance of Amnesty International as well as the Caribbean Institute for Human Rights so they could also play a part in the investigative process and to assist the victims of this incident."
Williams said that advocacy group International Parliament for Human Rights (PIDH) has also launched a separate investigation into the incident.
During an interview on Tuesday, Williams said after speaking with migrants, there were parts of their story that contradicted the official coast guard report.
He also said that two more migrants who were aboard the vessel were interviewed by lawyers as part of enquiries into the incident with coast guard officers that led to the shooting death of the child.
Williams also confirmed that the father of the child, Yermi Santoyo, was reunited with his two-year-old daughter Danna Santoyo at the UNHCR on Wednesday.
He said an interview was also facilitated with migrants and officials from the Caribbean Institute for Human Rights.
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