It doesn't have to be done during the first semester unless accommodations are being requested for that semester. But, it must be done before they can be considered. The institution has no responsibility to make accommodations retroactively. It is important that students provide documentation not only of a diagnosis of a physical or mental impairment but also of the functional impact of that impairment. This documentation must come in writing from a qualified professional.
Most institutions have guidelines for documentation, which is available upon request.
In most instances documentation should be recent. Obtain assessment and test results and provide them to that office. Post-secondary institutions will not provide students with testing or assessment for a learning disability. If a student feels that they have such a disability they will need to contact a qualified professional for assessment. In the case of a medical disability, students should submit documentation from a qualified medical professional stating the nature and severity of the disability, the diagnostic procedures used, and recommendations for academic assistance.