I can find actors and actresses of most races/ethnicity by using IMDB a public website. There is a part of the website that costs money but that is not the part I use. 

Step 1: Find one well known actor of the race/ethnicity that the character is.

• For example if I’m looking for an actor/actress that is South Asian in background I’ll go to Sendhil Ramamurthy’s IMDb page.

Step 2: On the side of most IMDb pages is a section called Related List. Click there.

Step 3: Look for a list that contains actors/actresses of a similar background.

FOR EXAMPLE:

These are the list I found from going to Sendhil Ramamurthy’s page.

This One

This One

This One

Look various list of actors and actress that are South Asian!!!

This can be done with almost any background (I haven’t tried it with all)

Let’s try Asian,Black,Latin@,and Native American.

Following the above steps I found these list…

Asian (went to Justin Chon’s page)

Here,Here,Here

Black (went to Shareeka Epps’ page)

Here,Here,Here

Latin@ (went to Sara Ramirez’s page)

Here,Here,Here

Native American (went to Irene Bedard’s page) 

Here,Here,Here

There are even list that are organized by body type,hair color,breast size, etc. 

Now keep in mind this is the way I do it. I use this method when I dreamcast. I have NO connections at all. I know no casting directors. I know no agencies. Don’t forget a little thing called a casting call. I have all these actors/actresses at the tip of my fingers. When big names say they looked but couldn’t find an actor or actress of a certain background I don’t buy it.