It depends on the volume of data. There are 2 options:
- send it to the client pre-emptively (perhaps as json or html) in the page source
- let the client query it based on their input
The second is common if the data-volume is non-trivial, as you can query when (for example) they've entered 3 characters; very useful for names and other long lists.
Re the web-service; this doesn't have to be a full/complex web-service; just a simple route or ashx (for example) that returns the filtered data.
The jquery autocomplete plugin supports both scenarios, although this is now partly obsoleted by jquery ui plugin.
Is it possible to implement autocomplete by looking up values from database in code behind
Well, that is at the server - so you're essentially talking about the same "web service" that you say you can't do... I also think you should separate out the 2 functions (create page vs provide auto-complete results) into separate files (/pages/whatever).