Dear aspirant,

Yeah it is necessary, the medical certificate should be issued by the government only.you can go any government hospital or CMO office.

Step by step guide:

Go to district hospital where CMO sits and Then get a prescription with your name.

Go back to CMO office where you will get a stamp on prescription. Then they will trick Mark the test which have to be done to get a certificate. 

For UPSEE they are 

1. Eye Test

2.ENT test

3.Orthopedic test

4.ECG

5.X-ray

Go to each department and get their stamp and after getting all the stamps again go to CMO office and there your certificate will be filled by them and they will also put the CMOs stamp. You will be charged some amount for this and there he / she will sign on your certificate and will keep the prescription along with your aaddhar card photocopy.

NOTE: they will see you aaddhar card for your identity verification. 

Hope the answer is helpful.

All the best!