All music styles are overlapping hybrids, so you consistently find elements of one in another.
However, there are identifiable characteristics of American Country Music, as long as you understand you will often see those very characteristics in blues, rock and roll and other popular forms with a common heritage.
Probably the most prominent feature would be the hammer on suspension from the second to the third degree of the scale. It is most often played with bent strings on guitar, or by pedal manipulation on a steel guitar or by a glissando on the fiddles. However, the country piano lives by this figure, as you will hear in the works of Floyd Cramer.
There are a number of characteristic rhythms that identify the form. I would leave that to a percussionist to describe well.
Because this form is grounded in rural folk music, the lyrics of songs concern themselves with the problems of rural people, or often the problems of rural people who have moved to the city. Nostalgia is a strong motif in Country songs.
The singing style typically includes scooping, in the manner of the 2-3 hammer on described above. The accent used by Country singers usually reflects a background from parts of the country with large farm populations - the rural south, the mid west and the southwest.
This is just a cursory review of a few of the characteristics of the form. It is interesting to note that the Father of Country Music is widely recognized as Jimmie Rogers, "The Singing Brakeman." One of three men with the same name in 20th Century Music, (the others were a wonderful Afro-American blues great, and a very popular white folk singer,) he recorded with the likes of Louis Armstrong and contributed almost as much to the origins of the blues as he did to the form he is said to have fathered.