Jarl Balgruuf, after getting a message from General Tullius in which some of Ulfric's plans were recorded, decided to send Ulfric his axe.
Since Ulfric Stormcloak saw those who weren't with him as against him, Balgruuf instantly ordered his steward to write a message to General Tullius, requesting Legionnaires.
Jarl Ulfric Stormcloak sent his axe to Whiterun, which Balgruuf returned, meaning he did not back the Stormcloaks. Shortly after Balgruuf got to know of this news, he declared his allegiance to the Empire, previously wishing to stay out of the war whenever possible. After an unknown period of time, Ulfric started planning an attack on Whiterun.
Jarl Balgruuf refused the Legion's right to garrison troops in Whiterun city, on the other hand he also refused to acknowledge Ulfric's claim. Whiterun Hold had been neutral territory during the Skyrim Civil War, with skirmishes on both sides taking place in the Hold and Fort Greymoor switching hands between the Empire and Stormcloaks on a regular basis.