While you could possibly setup three different datasources and switch out the data, I'd suggest setting these up in different workbooks.
Then you can have the DEV/STAGE/PROD flow for your workbook buildouts as well.
In our environment, we setup all of our environments as separate projects and then switch out the data connections as we move the workbooks up.
This is probably easiest using server hosted datasources.
Hope this helps!
I don't know the way to use "drop down list", but you can use replacing date function to switch the datasource.
However, replacing causes some trouble, so please pay attention.
This link helps well.
Thanks for your answer. First of all I need to query two databases at the same time to show a side by side comparison of data. The two databases could be same (prod vs prod) or different (prod vs staged/QA). Secondly, the end of user of this workbook will only have Tableau reader thus they will not have the capability of replacing database connection. Thus my original ask of using parameter to switch databases.
thanks again for your reply.