Sign with the P-Chain address for the following actions:

Importing from P -> C
Exporting from P -> C
Importing from C -> P
Self-bond Transaction

When Exporting from C-> P, sign with the C-Chain address.

In order to successfully transfer tokens from the C-Chain to the P-Chain, or vice versa, you must complete a two step process.  
The first step of a transfer is an Export transaction, which then must be followed up with an Import transaction.

If for example I wanted to transfer 10 AVAX from C-Chain to P-Chain, I would:

Sign and Broadcast an Export Transaction where the from_address is my EVM-Chain address and the to_address is my P-Chain address
Sign and Broadcast an Import Transaction where the from_address is my C-Chain address and the to_address is my P-Chain address

If I wanted to transfer 10 AVAX from P-Chain to C-Chain, then I would do the same two steps but switch the from_address and to_address.

201transaction created