I have sole physical custody and shared legal custody.

My son was recently hospitalized and had to have surgery to remove a coin he had swallowed and was stuck in his esophagus. This is the first (and hopefully only) time anything like this has happened. I contacted the father and told him where we were going and that he was having surgery. His father did not respond or try to contact me for at least 12 hours after I contacted him. He is now saying I withheld information about my son because I did not tell him step-by-step what was happening, and wants to get custody of him.
1) Hospitals have dead zones & don't want you to use your cell phone in certain areas.
2) I was holding my son the whole time to keep him from removing his IV or tilting his head back (they didn't want the coin to flip & block his breathing), and didn't have any chance to leave the hospital to make any calls.

Does he have any grounds to get law enforcement involved or have the courts change custody like he is threatening?

He has no grounds whatsoever. It was an emergency situation. You tried to contact him and from there its up to him to get to the hospital etc.

No, obviouly you two are having a lot of other issues about custody ?

I will assume you can prove you called him when it happened with a copy of your cell phone or home phone statement if it goes to court.

1. police have nothing to do with it, it is a civil family court custody issue

2. he can of course file either to have you in contempt or even ask for change ( he can do that without any major thing happening)

Even if you had this done as an emergany and did not tell him to after, he has little grounds for anything, but that does not stop him from trying in court if he wants to.

I contacted him before we went to the ER, as well as at the ER before they transferred us by ambulance to a children's hospital for the surgery. He knew where we were, and what was happening beforehand. My mother was with me as well, so she is witness that I did in fact contact him. When I did contact him, his response was "Well what am I supposed to do about it" in a sarcastic tone... apparently his concern was not there

His father lives in a house with 10 other people, and sleeps on a couch. When he does have him, he always comes back sick. He was willing to give me sole physical & legal custody until recently when I told him he needs to start paying child support.