Why couldn't you just deposit it with the state's central bank, which is what commercial banks do? Their cash balances are just numbers in an electronic ledger. There isn't some vault with physical cash inside and armed guards on the outside.
In the US, the answer is that the Fed says you can't. There's some good discussion on a recent attempt/request to change this at [0] (Scott Sumner), [1] (John Cochrane), and [2] (Matt Levine).
[0] https://www.econlib.org/why-does-the-fed-oppose-narrow-banki...
[1] https://johnhcochrane.blogspot.com/2019/03/fed-vs-narrow-ban...
[2] https://www.bloomberg.com/opinion/articles/2019-03-08/the-fe...
Because state central banks won't take you as a customer because they aren't commercial banks, aren't interested in being commercial banks, and are often legally prohibited from acting as commercial banks.
Also, because negative interest bond rates are produced by the same conditions which motivate negative central bank interest rates, so it's not much of a solution even if it was allowed. Bank deposits and bonds are both ways of loaning people cash you aren't currently using (but demand deposits mean it is legally expected for them to give money back on demand, so usually has lower interest due to the greater convenience.)
https://www.ecb.europa.eu/stats/policy_and_exchange_rates/ke...