When transferring credits do I need permission from the "leaving" university?

You should not take the term "transferring credits" so literally -- nothing is taken away from the (at that time) previous university. Instead, you are convincing the new university that you already obtained some parts of the education they are offering (so that it would be a waste of your and their time to do that again), and have the credits to prove it. The new university then awards you the appropriate credits according to their regulations (which might be more or less than the corresponding ones at your old university) based on their trust that you could in principle pass the modules again. The credits at your old university remain (at least for some time), should you decide to switch back.

One issue that occasionally comes up at US universities is that in order to transfer credits, the previous university has to send an official transcript to the new one. Many universities require that before they will send the transcript, you have to have paid all tuition and fees you owe them (or have financed them with a student loan). So if you are behind on tuition payments or even owe library fines, you may not be able to get the transcript you need.

Other than that, in my experience, there isn't any particular permission that you need in order to transfer.

Here in Chile it is up to the receiving institution to decide if they recognize previous work for credit or not. The original school has no say in the matter.