State of California. Here is the form that states you must sign off your medical records and all other records.
http://www.mbc.ca.gov/Forms/Applicants/application_forms_l1f.pdf
Also, would anxiety and PTSD that have been RESOLVED count as something that might interfere with my ability to practice safely?
California's Medical Board is particularly draconian, and during an investigation, they would likely request your medical records. However, this should not happen during a routine application and they will not look at your medical records per routine. In other words, something has to trigger an investigation, such as a positive criminal history on your background check, a leave of absence during medical training, or any prior disciplinary proceedings (and other red flags).
Basically, just look at the application form and see if you would have to answer yes to any of their questions that require further explanation:
http://www.mbc.ca.gov/Forms/Applicants/application_us-canada.pdf
They tend to be most uptight about any substance abuse issues and ask questions as to whether you have ever been treated for an addictive disorder or have been in a program. Anecdotally, I have seen people get a probationary license in CA due to a history of a DUI 10 years prior to application despite current prolonged sobriety and no patient care issues. I don't think that they would care about prior treated PTSD/anxiety unless there were coexisting substance abuse issues or it currently would affect your ability practice. The main issue would be if something bad happens during your time of medical practice related to your past issues and there is a patient or staff complaint, then the medical board would do an investigation and would likely get on your case for not revealing pertinent history to them during initial licensing - likely leading to more severe punishments due to additional charges of impaired professionalism and ethics.
Overall, do you think that you would have to truthfully answer "yes" to question 61? - not knowing the severity of your condition and it's current state, I cannot answer that for you.
Remember, the above is just an anecdotal account from a guy on a forum who has no official legal training and has no desire to ever practice law. If you have concerns about how to answer some of these questions or are unsure, contact a license law firm.