An autopsy on Brittany concluded she died from pneumonia, anemia and excessive use of prescription medications in December 2009.
Five months later her husband, Simon Monjak, also died, with the cause of death ruled as pneumonia and anemia.
Both Angelo and Brittany's mother, Sharon Murphy, believe the deaths were both caused by toxic mould.
Angelo said in a statement: "Years after my daughter's untimely death, toxicology testing on her hair still has not been completed. Office of the Los Angeles Coroner and the Los Angeles Police Department admitted that such tests were not done and refused to conduct them.
"At this point, I am asking the court to intervene and allow me to get the specimens independently tested. Brittany's hair and tissues were about to be destroyed, but I've paid to have them preserved, so that they could finally be examined. I'm not going to rest until my daughter's untimely demise is properly investigated, which hasn't happened so far. Her case deserves more than a superficial glance."
The suit has been filed less than a month after a Sharon filed a suit at Los Angeles Superior Court against a law firm which represented her in a case involving the Hollywood Hills home where she and her daughter lived.
Sharon insists defects in '8 Mile' star Brittany's Beverly Hills home led to her death and although she has previously accepted a settlement from builders for the faults in the property, she didn't realise she had waived her right to sue for wrongful death.