Nurses at the hospital mistakenly gave twins Thomas Boone and Zoe Grace 1,000 times the recommended dose of the blood thinner heparin, leaving them vulnerable to uncontrolled bleeding and leaving them, for a time, in critical condition.
Cedars-Sinai Medical Center was not sued, though the hospital was described in a court filing as a "potential defendant."
Hospital officials have cited at least three safety lapses that led to the overdoses.
The couple has a pending lawsuit against Baxter Healthcare Corp., alleging that the labeling and design of heparin led to the massive overdose. The suit alleges that the company knew other infants had died as a result of errors involving the drug but failed to recall the high-concentration vials.