The answer depends on a lot of factors. For one, not all 3 year olds are ready to be potty trained. You said he doesn't have accidents at school so that lets me know that he is ready. You should be aware however, that at 3 years old he will have accidents, mostly at home since that is where he spends most of his time. I have 4 year old twin boys and although they do still have accidents they have perfected the skills at school! If he is wetting mainly at night I would just buy him some pull ups or protective vinyl underwear covers. Make sure to leave a night light on in the hallway and bathroom in case he is afraid of going in the dark. I am unsure by your question if he has accidents or just refuses to use the potty at home. If he is just having accidents it is probably due to not getting there on time. He knows he has to go, but waits too long. (That's the problem I have with my boys). In that case, in my opinion, time alone will resolve the problem. On the other hand, if he just refuses to go period, it will take more digging to find out the cause. The solution to the problem will be found within the cause. If there is something in the bathroom that is scaring him, remove it. If he doesn't want to go alone explain to him that you will go with him until he asks you not to. Talk to your son and maybe he will open up. I am sure you have spoken to him, but make it a point to mention it very frequently and eventually he may open up and tell you what is bothering him about using the potty.

I have 4 kids with a 5 year age difference. What I found worked with my youngest was to reward him with something every time he used the "big toilet". It could be a M&M or a fruit snack or something he likes. Then I had the older kids help and encourage my youngest son. If their help resulted in a successful use of the toilet, then they got rewarded too!

All kids are different.Be patient and don't yell at your child for any reason.Talk to him nicely and eventually he or she will understand sooner or later.