I am about to complete a Ph.D. in Hong Kong and would like to study in the United States. I hold a first class B.Eng. degree in Electrical Engineering. I have a CGPA of 3.67 out of 4 in my current PhD studies, two journal publications (IEEE Transactions) with two more to be submitted soon. I would consider this a fairly good academic record.
For career purposes, I would like to obtain a Ph.D. degree (in a different but related field) from a top American university. There aren't post-doc openings in my current research area, which is why I am considering another PhD in a related area.
Question: Is it considered illegal to not mention that I hold a Ph.D. (hopefully) during application? I noticed some schools frown at what some would call a "professional" or "serial" student.
NB: I have read responses on this question and I am satisfied with them. But I feel there's need to make my question clearer for those who did not understand. Some universities clearly state on their websites that they will not consider applicants who already hold a Ph.D. while some others do not specify this. My question was more for the latter. But now I know that other than dealing with the university, it will require lying on visa application, as some people wrote below.
Thank you all for your contributions.