Murray is serving a four-year prison sentence for his role in the 2009 death of Michael Jackson.
The appeal centers on a bottle of the anesthetic propofol. Murray's lawyers want a test of residue found in the bottle.
Jackson died of a propofol overdose while in Murray's care. The lawyers argue that if it comes up as 100 percent propofol, it would support their theory that Jackson gave himself a fatal injection of the drug.
