Probably the police wants to gather some evidence. The easiest way to block a wifi tap is to change the wifi password... or wifi name. Both things will be noticed by the eavesdropper because they will block the device *but* it is an easy way to block it asap.

What I would do:

1 - Get an old android phone. 2 - Configure the phone to act as an access point with the same wifi name and password. 3 - Change the wifi password or name in the router. 4 - Change wifi passwords in laptop, etc... (I know, it is a pain). 4 - Activate the phone access point. 5 - * IF * the listening device connects to the phone AP wifi, you know there's a wifi tap. You can connect the phone to your home wifi later... and it will look transparent to the stalker.

Best of luck with this situation.

Some routers can block internet access for new/specific devices. You could try to find the correct device by blocking them all and unblock them after finding and checking them. One possibility is that the stalker uses an old android. That would harder to detect, since its possible that the device is not connected via wifi.