Generally to euthanize a mouse you inject directly into the heart or even into the peritoneal belly. However, this is sounds more brutal hence keeping euthanasia pain free is as easy as insisting that your pet be knocked out with the help of an inhalant anaesthesia previous to being given any lethal injections. A serious vaccination may not even be required if the rat or mouse is given an overdose of the anaesthesia. Anaesthesia overdose is also a process that can be very easily at home.
On the other hand, I would not even think about euthanizing a mouse at home with the help of any other process than anaesthesia overdose. I consider this as the only humane technique, in my view. Let me give details on this procedure. You can hold the rat and pet it like any other animal does. Once the rat is comfortable pour some Halothane on some cotton balls. And place it right next to his nose. Then later move away and he will die slowly and I am sure it will not be painful for both.
On the other hand, I would not even think about euthanizing a mouse at home with the help of any other process than anaesthesia overdose. I consider this as the only humane technique, in my view. Let me give details on this procedure. You can hold the rat and pet it like any other animal does. Once the rat is comfortable pour some Halothane on some cotton balls. And place it right next to his nose. Then later move away and he will die slowly and I am sure it will not be painful for both.