It depends on the problems. To get hired, you typically have to pass a medical examination.
Things like having seizures, or a severe heart or lung condition may prevent you from becoming a police officer. The majority of typical applicants meet the medical requirements. You will be prevented from becoming a police officer only if your physical or mental condition would significantly interfere with the performance of the job. Each law enforcement agency has different medical requirements, based on its essential job functions. As an applicant, you will have an individualized assessment to determine whether you should be hired.
If you have a serious medical condition, before you invest the time and effort in applying for a job, you may wish to consult your own physician about the extent to which it might affect your ability to perform that job.