When I use Runtastic and track my run on my Apple Watch, do I double my distance in the Health app? When I use RunTastic to track my run on my iPhone and also use the Apple Watch health app to track my run (or not), is the resulting data which is sent to the Health app doubled?

For example, if I run 1 mile (and track it on Runtastic and my Apple Watch), would I see 2 miles in the Health app?
I've used several apps and you do need to pay attention to which apps read from health app and which write to it.

In practice, it's pretty easy to take a screen shot of the Show All Data screen from within the Health app for Walking and Running Distance for example. Then operate the apps and enter an exercise period and repeat the screen shot after the workout is complete.

You will want to examine the hour surrounding a 5k run, for example, to be sure that your phone and watch alone are not "double dipping" if you have both on you when you run. Adding a third party app in addition to the settings you may have enabled on iOS and watchOS could triple the data.

Also, be aware that code can change so even if your app isn't duplicating data now, you'll want to sanity check things periodically in case the developer of the app changes how it reads and writes to the health database.

It's easy to go in and clean up a day's worth of double counted data, but you'll likely need an automated tool if you find out weeks or months of data isn't counted the way you prefer.