Logistic regression usually chooses the class that has the highest probability. Working on 2 classes, the threshold is 0.5: if P(Y=0) > 0.5 then obviously P(Y=0) > P(Y=1). The same stands for the multiclass setting, it chooses the class with the biggest probability
There are thresholds that only affect the proportion of false positives/false negatives, but it is not the parameter of the LR model.
Hope this answer helps you!
Learn more about Logistic Regression by watching this video tutorial: