SDL Tridion publishing is (currently) not version based, which means that at the time an item is published, its latest (checked in) version is used when the item is rendered. The actual version number the item had that that time is not stored somewhere, so there also is no direct way of retrieving that via the API.

What you could do is write some code which checks the version history of the item, and through that determine what version was possibly published. I deliberately say possibly, since if there are items removed from history, you might not get a correct result back.

SDL Tridion publishing is (currently) not version based, which means that at the time an item is published, its latest (checked in) version is used when the item is rendered. The actual version number the item had that that time is not stored on the CM side, so there also is no direct way of retrieving that via the TOM.NET API.

What you could do is write some code which checks the version history of the item, and through that determine what version was possibly published. I deliberately say possibly, since if there are items removed from history, you might not get a correct result back.

Update

As Frank was smart enough to comment, indeed the version of each published item is actually sent along to the Content Delivery side and stored in the Broker storage (in the Items table to be specific).

So you could revert to checking the Content Delivery API, to see if you can determine the version information from there. I didn't bother checking what APIs are available for you on that side ;o)