According to the police report, obtained by TMZ, Griffith's sister called Vegas cops Wednesday night to report the incident. Officers say when they arrived, Nathan was outside the home yelling, saying he never touched his sister ... he also allegedly smelled like booze.

However, when cops made contact with Griffith's sister, they observed visible red marks on her neck and redness on her eyelids -- indicative of someone who had been strangled.

Cops say Nathan's sister was scared and frantic as she described what happened -- alleging Nathan got pissed when she called him out for his aggressive past with his family and significant others.

The sister says Nathan grabbed her by the throat, pushed her down onto the kitchen floor and got on top of her -- releasing his grip at times to give her some oxygen before tightening his grip again -- while allegedly stating, "You're going to submit to me."

The claims and evidence were good enough for officers ... who arrested Nathan for battery by strangulation.

However, they say during transport Nathan was banging his head into a rear window and making suicidal statements ... and screaming and yelling while he was booked.

Nathan and Jenelle Evans have one child together, a son, but called off their engagement years ago.