Is asking for a "Chinese menu" in a Chinese restaurant a common way to get more authentic dishes?
I am answering the question as I understand it based on our discussion in comments.

Step 1 - Choose the restaurant wisely. As a rule you don't want big fancy restaurants and you certainly don't want to even try in a chain restaurant. You want the holes in the wall run by members of the ethnic group that matches the cuisine. When you enter the restaurant, listen to the ambient sounds of conversation (customers and staff), the more you hear the language that matches the cuisine, the better your odds.

Step 2 - Be super friendly, smile a lot and ask lots of questions about the cuisine and the menu.

Step 3 - Be honest, upfront and clear. Tell your server that you really want to experience the cuisine that is the specialty of the restaurant. If the restaurant is Thai, for instance, ask what the most popular menu items are for Thai customers. Now ask if there is a special menu for Thai (or Chinese, or Spanish, or whatever) customers. There may be, if there is one your server will most likely be happy to get you one. You may or may not be able to read it. See step 2 again. Even if there is no special menu, by now your server most likely understands what you want.

Step 4 - Simply ask for what you want. Ask if the cook or chef can make you a meal that is like what would actually be served in the country in question. You may be able to specify, "Really authentic Pad Thai like I'd get on the street in Bangkok" or you may be even luckier and have no idea what you're going to get until it arrives. Either way, express your appreciation that they are allowing you to order "off menu", and be sure to mention that you don't mind a bit of an extra wait.

Step 5 - If you are in a part of the world that doesn't consider tipping to be strange or offensive, tip very generously.

Step 6 - Be brave.

If the restaurant has a bar, do all of the above but have your chat with the bartender. 

That's it. I have quite a bit of experience getting authentic food in restaurants with dumbed-down menus. Those steps will work more often than not.

One final note. If the cuisine in question is often hot/spicy, be sure to tell your server about your preferences in that matter particularly if you're sensitive to heat. If you're successful getting authentic food, it would be a shame if you couldn't eat it. If you love heat, be sure to tell them that too. They may hold back a bit otherwise.