Auditors from the German Doctors' Association (BÄK) found "widespread" irregularities in the transplant system, the Süddeutsche Zeitung (SZ) reported on Thursday.
Prosecutors in the world-famous university town have opened an "investigation into suspicion of attempted grievous bodily harm through manipulation of heart transplant patients' waiting lists," they told SZ.
They have removed a number of patient files from the hospital and are still working through them to identify suspicious cases.
The hospital confirmed to the SZ that a total of 34 patients who underwent transplants in 2010 and 2011 had "heart transplant reports that didn't completely comply with the guidelines of the BÄZ."
Doctors are believed to have tampered with patients' files to make them appear more unwell and move them up heart transplant waiting lists.
Now the hospital says it is working with the authorities to clear up the allegations, and has itself filed charges against those responsible.
Irregularities in transplants in Heidelberg are just the latest in a series of cases that have also hit hospitals in Berlin and Munich in recent years.
Doctors bucking the rules
Transplant doctors are often tempted to bend the rules in their patients' favour when the sick don't meet the strict criteria set out by the authorities, Christian Zimmermann, president of the German Patients' Association (APV) told The Local.
"Of course I'm sympathetic to the doctors, but I don't agree with what they've done," Zimmermann said.
"They depart from the guidelines not out of financial interest, but because they disagree with the rules.
"Instead, they ought to protest and say out loud that they disagree, go to the ethics commission and have a public debate," he said.
Zimmermann is concerned that repeated scandals over organ transplantation will reduce the number of people willing to donate their tissue after their death.
An official German organ donor card. Photo: DPA
The ethical questions doctors face about which recipients should get priority are never going to be fully resolved - for example, whether young people should come before the old or whether those with 'lifestyle' diseases, like liver cirrhosis caused by alcoholism, should be at the back of the queue.
That's why "there should be a 'corridor' with some margin for doctors to have input into decisions, rather than a rigid set of rules," Zimmermann said.
At the moment, "doctors are exposing themselves to prosecution for murder or manslaughter, with serious legal consequences, and causing serious doubts among the general public," he added.