In Germany, people are allowed to commit suicide.
There is no obligation to live.
Unless there is a DNR or other express statement that Alice does not want nobody to come to her rescue (and it does not matter whether you were aware of such statement):
- Ex lege, by law, there is now a contract between you and Alice.
This kind of contract is called Geschäftsführung ohne Auftrag, agency
without specific authorization, § 677 ff. BGB.
- You have to act in the interest of Alice as you knew at the point in time you acquired the spare key.
It is irrelevant to you if you learned later Betty would be a better person to steward the key.
The GoA, the statutory contract, your duties and rights, is completely defined when you got the key.
- It is your duty to keep the key, maintain the apartment, (feed pets?) and eventually return the key.
You are allowed to use assistants, e. g. Betty could become an assistant, but this does not terminate the contract between you and Alice, so legally all duties remain yours.
- Since holding Alice’s key had the purpose to prevent imminent danger from happening to Alice, you can enjoy the liability privilege of § 680 BGB:
Only gross negligence and deliberate intent warrant damages.
For instance, if the court found your choice of an assistant was deliberately poor or grossly negligent, you’d be liable.
Frankly, keep it simple:
The police ain’t no trained lawyers.
They never heard of echte berechtigte GoA during their training.
If you go to the station, ask/say “I know a friend who …” (without giving too many details).
Otherwise, I’m afraid the officers might make a huge deal out of it, but maybe simply task you to keep the key.
And it’s a bit of a different issue if an officer orders you to do something on behalf of the state.