No, it's not Texas City, Texas; it's a small town near Dallas with a name that says a lot without saying anything. Mildly displayed toughness that is quintessential "Texas".
Gunfights were pretty common in 1800's era Texas. The biggest one in Texas however wasn't between the town sheriff and some outlaws, it was between cops and student protestors.
Between December, 1884 and December, 1885 ... about 3 years before Jack The Ripper did his thing in London ... 8 girls were attacked, raped and murdered in Austin, Texas.