The first thing to determine is where the money sent over come from and the second is if the money is an assessable income or not, if the money come from social security, pension, interests, dividends etc. This will determine if you need to file but also if you need to pay any tax according to the double tax agreement and after Thai allowances and deductions.
If you have already paid tax in the US on the money sent over, you will most likely not have to pay any tax in Thailand, but you may still have file. Go over to the local revenue branch and explain to them, with a bit of luck they might tell you that you don't even have to file or that you have to file but not pay any tax.