Can I take my friend to court if I sign for her apartment lease but she broke the lease?

Unless you and your friend have your own separate agreement (preferably in writing or some other "good" evidence) regarding the duties/liabilities of each other in such a scenario, your signing on as a cosigner is agreeing to be just as liable to the landlord as she, and just as a backup as some people thing. Landlord can go after who ever is listed on the lease and since there is nothing improper with that, there doesn't seem to be any good grounds to then turn around and try to recover from her for the same.