Thank you for getting back to me. 
The taxonomy I created in one post type is not able to map with the other post type.  I have Expertise information as a taxonomy in Law expert post type. I have added a relationship between Law expert Post type and Cities Post type and chose Expertise information as a custom field. 
But I think custom coding is the best option as you suggested.
Keeping that aside, I m now facing a new issue. 
As I stated earlier I have Law experts who work at multiple locations with multiple expertise.  
One expert can be a child custody lawyer in NY and Divorce lawyer in Brooklyn.  
I would like to display experts available based on the location or expertise information the consumer chooses. 
To achieve this I have created 4 Post types: 
1. Law Experts (information such as phone, email, picture, description, expertise info etc)
2. States
3. Counties
4. Cities
I have created relationships between States -> Counties, Counties -> Cities, Cities ->Law Experts. 
While creating a relationship between Cities and Law experts, I chose the expertise info field in the Law Experts as the Custom field (PFA one.png). 
I am displaying the Expertise info on the search page along with State->Counties->Cities dropdown. (PFA two.png)
This information mapping such as city, county, expertise info is appearing on the Law Experts as PFA three.png
However, when I am displaying expertise info as the dropdown on the search page I am unable to see the mapped expert info. I am only able to see 'All' as an option PFA four.png. 
I would like to display all the expertise information (PFA five.png) on the filed on the dropdown. Please suggest. 
Thank you.