Jury duty on Monday morning at 9am but i work overnight?

at the fire department doing dispatch from 9pm to 9am. Should my job allow me to leave early so i can get some rest and get paid for that time im out w/o using my personal leave? The last time we had a different schedule I worked nights that time too but I went in at 6pm and got out at 6am. I told my supervisor I had jury duty and she said that I had plenty of time to get there since I got out at 6am. That wasnt the point, I was falling asleep in the courthouse and driving home I felt like I was driving drunk. I was up for at least 26hrs