BERLIN, March 22 (Reuters) - Germany is planning additional spending of 5.8 billion euros for coronavirus tests, vaccinations at family doctors and hospital emergency aid as Europe’s most populous country is failing to contain a third wave of infections, a document showed on Monday. The health ministry asked the finance ministry to make available 3.3 billion euros to offer free tests for citizens, 1.5 billion euros to enable family doctors to offer vaccinations and 1 billion euros of emergency aid for hospitals, a finance ministry document sent to lawmakers showed. Germany is working on a debt-financed supplementary budget of more than 60 billion euros which will push up net new borrowing this year to a record high of over 240 billion euros, two sources told Reuters on Friday. (Reporting by Michael Nienaber and Holger Hansen Editing by Riham Alkousaa)