Toliver was a member of the Slovakian women's national basketball team in the EuroBasket Women 2015 qualification tournament in 2014 after receiving her Slovak citizenship. The team finished first place in Group A to qualify for the EuroBasket Women 2015 tournament, where they finished 9th place with a 3–4 record, missing out on a spot in the Olympic qualifying tournament for the 2016 Summer Olympics.