As the old proverb says that 

music is medicine of mind, which  never ever been found to be incorrect, hence no need discussion among scientists working in the area of psychiatric disorders.

It depends on the aims of the music therapy and the pathology of the client. If a client is referred following stroke to encourage fine motor skill re-development, reliable physical assessment tools would exist to be able to give a pre- and post-therapy measure (though there's also the question of whether MT is having an effect independent of standard treatment/care...there are a few RCTs, but more would be lovely). Depression symptoms can likewise be quantified through psychological tests pre- and post-therapy; whereas if a child with autism is referred to encourage social skill development, there's not really a standardized measure that can be used. If therapeutic aims are strictly musical, it's usually up to the therapist. Many may have individual scales or infer efficacy from qualitative session descriptions, but there's no one measure for music therapy's efficacy. Did you have a specific client group in mind?

Dear Jenn,

Music therapy has a different results in different client.

For example you can see one of my articles in title of:

Music Therapy Reduces the Intensity of Pain Among Patients With Cancer.

Regards,

In my work at a mental health hospital, outcomes are measured the same as other disciplines... reduced symptoms, reduced readmission rates, reduced falls, reduced infection etc.  As an example, I have attached a research trial I did in 2005 looking at the effects of music therapy in dementia.  There, my clinical goal was to reduce or reverse cognitive decline, as assessed by blinded assessors and in comparison to a control group who did not receive the music therapy.

No Doubt , nature has kept some remedy for each disease but we have to find it, it may be form music world plant animal river ocean

One approach is to consider music's impact on brain waves- changes to brain waves can be used to infer the relaxation therapeutic effects of music.

Article Modulation of EEG Theta Band Signal Complexity by Music Therapy