I would like to know if a person has to be currently working as a project manager when applying for PMP certification.
Obtaining or holding a current PMP certification from the PMI does not require that the person is currently employed. However, to obtain the certification the applicant must provide evidence of three years of work experience in the knowledge domains tested.
The full criteria for applying for the PMP can be found here on the PMI Website's Certification page.
The certificate holder must keep current in the field over three years by continuing professional development through events or formal education. Otherwise the certification become expired and a new application and testing process must be completed.
No you do not have to work as PM.
You may have never got the title as PM before applying but as Polymath answered you have to show proof that you have the necessary expertise in the knowledge domains.
You will fill out a form, while applying for exam, in which you will state how many hours you have worked on each knowledge field on each and every project you have worked on.
You need to have 4500 hours of PM experience in a leading & directing role to to do PMP. So, PM role is must before doing PMP. However, PM role is not equivalent to PM designation/title. PM role means that you should have managed full or part of a project. Your role in the project could be of vendor management, team management, client management etc. The projects could be related to any industry. They could be big or small, technical or non-technical etc.
For any kind of certifications, there are some limitations, but it's not compulsory that you have to be in working in the same field. But to write any certifications you need to have proper experience with the education.
Now when you have raised as you need to be PM job so its not that necessary. There are larger benefits to grow when you want to be in Project Management stream. PMP is one of the best professional credentials in the field of Project Management. The benefits of PMP Certification are immense! Not only will you become a more complete person, you will become a better project manager. Some benefits, if I could tell you is: Growth in career prospects, enhancing your marketability, improving your project management skills, and last but not the least, increased earnings.
I am planning to take this is up as it is very important when we have plans for abroad opportunities!