The grand jury had decided there was insufficient evidence to bring criminal charges after Kris Harrison said the Glock handgun discharged accidentally while he was showing it to his daughter.
In February, a coroner in England concluded Lucy had been unlawfully killed, finding that her father’s actions amounted to gross negligence manslaughter under UK law.
Police in Texas have, however, said they would not reopen the investigation.
Evans said the force was “ultimately constrained by legal, jurisdictional and practical realities that significantly limit what any police force in England and Wales can do in relation to a death that occurred in the United States,” he said.
Given the “unusual circumstances reported” of Lucy’s death, a Senior Investigating Officer had been tasked with looking into the case.
That officer appointed a Family Liaison Officer and sought information from the relevant United States law enforcement agencies.
He said that despite the “clear jurisdictional limitations,” the force’s actions “reflected our recognition of the exceptional circumstances of the case and our commitment to providing whatever support and assistance was realistically available.”
The family had argued that as Kris Harrison is a British citizen, a mechanism exists under certain circumstances, where those from the United Kingdom who commit murder or manslaughter, can be prosecuted before British courts.