This Problem does occur without alt tabbing.
To be more specific, I normally tab out a few times during my game sessions but the bug even occurs hours or many minutes later.

In T123425#1576151, @Geez wrote:

Hello Burli and thank you for the report.
Does the issue occur only upon alt tabbing back into the game, or does the issue occur also without alt tabbing?
Regards,
Geez

Hi. This has been an issue for a long time in DayZ (might be from the very start?). The game fails to capture the player unpressing the attack button (probably due to an FPS spike or something like that) and never performs a manual check to see if the button is still pressed. I wonder if the new player controller addresses this.

While we're at it, in 0.61 there's an issue where often when you connect to a server, the game thinks you're holding the attack button (probably due to pressing "Connect/Play" and the game not capturing the release of the button) so once you connect you can't put it down until you tap the attack button again and the game finally registers the release.