As with most national parks, your primary safety concern has less to do with threats from your fellow travelers and more to do with the elements and wildlife. 

Unless you're near a lodge or visitor center, you'll find very few facilities in the park. Always carry plenty of food and water with you if you're hiking, and plan to fill up the gas tank before you enter the park (there are no gas stations located within the park). You'll also want to carry a map (which you can find at any one of the park's visitor centers), as you cannot rely on cell service within the park. 

Unless you are very familiar with the area, never hike or camp alone. Speaking of hiking, stay alert to avoid steep terrain and be especially careful near any of the park's lakes or streams. According to the National Park Service, water is the No. 1 cause of fatalities in the park. Wildlife, especially bears and mountain lions, can be another safety concern. Never approach animals, make plenty of noise when hiking, carry bear spray and secure your food and garbage. For more information on safety tips, consult the NPS website.