• No, you cannot have more than one domicile certificate at a time. It can be made only in one state and obtaining more than one domicile certificate is an offence.
• Domicile/Residence Certificate is issued to prove that the person bearing the certificate is a resident of the state or union territory by which the certificate is being issued. This certificate is required as a proof of residence to avail domicile or resident quotas.
  
  So, in your case you can get a domicile certificate for either of the states but not for both.

https://university.careers360.com/colleges/list-of-universities-in-jharkhand

and

https://university.careers360.com/colleges/list-of-universities-in-bihar

Hope this information will help