No, you don’t and discrimination law prohibits employers from refusing to offer you a job on the basis of a ‘disability’.
If your employer asks you to undergo a medical test prior to offering you employment, you do not need to disclose your disability unless it directly relates to the genuine requirements of your job. An important point is that these tests have to be given to all job applicants and employees, not just to anyone an employer thinks may have a disability or injury.
You should not mislead an employer or provide false information. A better option is to write ‘not applicable’ with respect to any form that asks you to disclose an injury that will not impact on your ability to perform the requirements of the job.
However, because an employer must make reasonable adjustments to assist you to perform the genuine and reasonable requirements of a job (provided to do so would not cause unjustifiable hardship to your employer’s business), you may choose to tell a new employer about your injury to allow for such workplace modifications to occur.
An employer is allowed to refuse a job to a person with a disability if it is to protect the health, safety or property of someone. However, this is a last resort and to avoid discrimination, an employer should really consider if there are any alternatives to this action.