What is troy built tb 32 EC gas oil mix ratio?

Probably 40:1 or 50:1 two cycle oil mixed into one gallon of gasoline.

This model is a four cycle engine meaning that it does not a mix of gas and 2 cycle oil. You just fill it like your lawn mower, gas and fill the crank case with oil

Two cycle engines run on a mixture of gasoline and oil. Each engine type is designed to run on a specific gas-to-oil mix ratio.
IMPORTANT: Use only oil that is labeled for use in "Two-cycle" or "Two-stroke" engines. Home Depot and other stores now have "premixed fuel" of gas and 2 cycle oil.
To mix two-cycle fuel, start by putting correct amount of oil in gas can. Then slowly add correct amount of gasoline. Do not try to mix gas and oil directly in gas tank of equipment.

IMPORTANT: Do not use any fuel that is over 30 days old. Do not mix more fuel than you are likely to use in a month. Old fuel can gum carburetors and prevent starting. Always use fresh fuel.

The chart below shows correct amount of oil per gallon that each mixing ratio requires. Expect that yours will be between 32 gas to1 oil and 50 to 1. 32:1 and 50:1 are most popular.
Ratio GAS:OIL UNITED STATES OIL per 1 U.S. GALLON Gasoline
(128 oz.) *INTERNATIONAL OIL per 1 IMPERIAL GALLON Gasoline
(160 oz.) *INTERNATIONAL OIL per 1 LITER Gasoline
(metric) 32:1 4 oz. 5 oz. 31.25 mL 40:1 3.2 oz. 4 oz. 25 mL 50:1 2.6 oz. 3.2 oz. 20 mL

use 2 stroke oil for 2 strokes, properly mixed with gas. should be a small engine type oil not out board or skidoo.

If it is a 2 cycle motor, then use an appropriate 2 cycle oil. I use a synthetic oil that 1 bottle is mixed with 1 gallon of fresh gas.

Oil runs back out of the carburetor air filter intake if I fill to oil level indicator on no oil gas mix engine. Anything wrong or am I just over filling the oil?

I always suggest using a full synthetic 2 stroke oil for these machines. It provides superior lubrication qualities and burns cleaner than conventional oil. The fuel/oil mix ratio is 40:1. That is 3.2 ounces of oil mixed in 1 US gallon of gas. Half that to mix up a 1/2 gallon. You can find this info and more in your manual. The fuel info is located on page 10.
http://dl.owneriq.net/d/dcedfb0b-6611-4152-bbbf-d793d087365e.pdf
You will need Adobe Reader installed on your computer to view your manual as it is in PDF format. If you don't have it, you can get a free download from their site. It is safe.

4 cycle engines do not run on mixed fuel. Run on straight fuel. They have a spot to put oil in just like a lawn mover, and should be changed regularly. @ stroke engines run on mixed fuel.

Straight Gas no mix for a 4 cycle.

Troy-Bilt products now are usually produced by Mtd, the ratio being 40:1.
However since John Deere made yours I'm 99.9% sure it should by 32:1.
In any case any power equipment you own (including Dolmar or Stihl) that takes an oill/gas mix benefits in the long run from using the richer 32:1 ratio. It protects the piston and cylinder much better, giving your equipment longer life. Do not use the "one mix for all" that you find at retail stores as it has been my experience it really isn't "one mix for all". Seen a lot of scratched pistons and broken rings from people using that.