This is the straight skinny, and I know everything, so forget what everyone else says because none of them know squat compared to me. I even tell the local police what the law says.
In Texas all motor vehicles are considered self propelled. Read that again, and understand it. Self propelled means, that with the motor running, you can just ride it off totally under it's own power from a stop. If you can't do that, it's not self propelled, so it's not a motor vehicle. If it's not considered a motor vehicle, you don't need a license for it. It doesn't make any difference what size the motor is.
A car is self propelled. A motorcycle is self propelled. A moped is self propelled. A motor bicycle is ???????? maybe, maybe not self propelled. That's why it's a gray area.
Texas law makes no specific mention of gas powered motor bicycles.
A typical china girl style motor bicycle, cannot ride off from a dead stop totally under it's own power. They must be peddled up to at least a few mph before letting the clutch out. That's what makes them legal. I talked this point over with the head of the, TDOT motorcycle safety division in Austin, and they told me that's what makes it a gray area in Texas law. They said as far as they're concerned it's up to each locality to decide what to do about enforcement.
The reality is we ride free all over the state without harassment. I live in Dallas, and ride in 7 local cities with no problems in 2 years. If you should get a ticket it will probably be for riding an unregistered moped. If you pay the ticket they will take your money. If you challenge the ticket it will most likely be dismissed without comment. No prosecutor wants to take a chance on losing a court action, and setting precedent for the entire state. At the time I talked to the TDOT they told me there had never been a conviction in Texas for riding a MB.
Some people will tell you about a moped under 50cc is legal, but that law was changed last January, and never applied to us anyway.
You might like to browse my Texas thread.
http://motorbicycling.com/showthread.php?t=26328