Currently there is no easy way to do that using the CLI or API, but enhancement request for this exists and will be addressed in the future.
Dividend information can be obtained through Counterparty block explorer sites. In case of blockscan.com, that would be the Dividends tab on their asset info page: http://www.counterpartyexplorer.com/assetInfo.aspx?q=ASSETNAME (replace ASSETNAME with the name you want to check).
Developers can use Sqlite to query the Counterparty DB for this information.