Input for liablity arise form income (parking charges)

Input tax credits is available to discharge the liability over output service, but in your example where is output tax service? If you are charging service tax over some bills, then yes, the credits can be utilized.

my question is 

can we adjust ITC of Hospital with the output of arising from Parking service provided, which is attached to hospital

I repeat, If you are charging/collecting service tax on any of your bills, and paying the same to department, then yes, you can take ITC over parking charges.

Yes Hospital providing parking service

"Is hospital providing parking service ?"

Basic question here is, though hospital is providing parking service to its patients/staff, but does it collect parking charges from them? and specifically, service tax over it????????????

"yes they are collecting the parking charges and charge the service tax over it"

A big confusion here is, they means who? Hospital!  I mean, hospital is payer or parking charges collector !!

Hospital is parking charges collector

and i wanna know whether can we cosider parking service in helathcare serice which is expemt under E/N 25/2012

No. Parking service is not tax-exempt to anyone, whosoever it may be!!!!!!