When a person has a legal duty, they should not be able to use their religious beliefs as an excuse not to fulfill that duty. Many people don't agree with various laws: they still have to follow them. A Catholic doctor that has a legal duty to assist someone needs to do so, regardless of their religious belief.
That doctor doesn't understand what it is to be Catholic. Such behavior is contrary to Catholic teaching. There is nothing in the Church's stance against contraception which prohibits rendering aid to those in need. This is the kind of behavior by low information Catholics which makes my religion look bad. That argument will not protect her on religious ground in court, either, because even if the court wanted to give deference to her based on Catholicism, this isn't it!
He is working in a profession that has nothing to do with religion. He cannot violate secular law and cannot use his freedom of religion to oppress another person's right to life, liberty, and property. This is a shameless and immoral act, and legal action must be brought upon him.
By the doctor turning away a bleeding woman, he has essentially committed a criminal act by allowing further harm to happen to a patient. Although the doctor is free to have his own religious beliefs, there has to be a separation of his beliefs from his obligation as a medical professional. This is a case where separation of church and state can be applied, since he must treat patients regardless of what his religious belief system since he works for a government run establishment.
There's no reason to get law enforcement involved in this case. Stupid decisions aren't always against the law. That said, this guy should immediately be asked to change positions so that he doesn't have to deal with this type of "moral issue" ever again. Maybe let him clean the bathrooms after everybody else is asleep.
Medical professions are part of very few that require certain actions due to every citizen's right to proper healthcare. Despite his personal religion, this doctor is bound not only by indutry-specific standards but statutory requirements due to his chosen profession. If this physician knew that his personal beliefs were so strong as to cause a moral quandry with his work, there are certainly many other fields of occupation that would not put him in that position.
He is working in a private sector. This question does not hold enough information, and to just say all doctors should be charged if x, is completely wrong.
If it happens during an emergency visit, that is one thing. If it happens, because a doctor is uncomfortable with the situation, and he deems it non-emergent and that she should get a second opinion, he should, and does have the right to do so.
Same thing is she walks into a private practice. All private hospitals have, and should maintain the right to run their business as they see fit.
A doctor should not be forced to take any patient in a non emergency situation.
He should not be charged for religious beliefs, it is not illegal to hold religious beliefs, he should not be stripped of his licenses, he should be dealt with by the governing body of the hospital.
No where does this debate imply this is a life threatening emergency, and to burn a doctor at the stake, strip him of his license, and criminally charge him to do something he is uncomfortable with is 100% wrong.