Good question...Caesar did not need the crown, his power was nearly limitless and the crown would serve only as an unnecessary symbol. His refusal could have also served to satisfy the Roman people that he was not an ambitious leader.
Even though caesar had already wield power over Rome and acceptnig the crown would make no difference he still refused to take the crown inorder to show the plebians that he was not interested in honours and praises ( however he initailly was working on becoming a dictator).
Since the time of the Roman King Tarquin Superbus, (Tarquin the Proud) Romans have always hated to have a king (rex in Latin). This is because he abused a married Roman woman called Lucretia who later killed herself to save her family from the shame. She then became the perfect Roman example of virtue and faithfulness. Shakespeare also wrote a play about this called The Rape of Lucrece. Brutus' ancestor, also called Brutus, drove out the Tarquins from Rome. Therefore, it is appropriate that his descendant should kill Caesar, also in order to protect the Republic from a potentially power-abusing tyrant. Therefore, if Julius Caesar accepted the crown, it would seem to people that he was setting himself up to be king. Later, after the civil war ends and Octavian (later Augustus) became the first Republican emperor, he was also presented with a crown at his inauguration ceremony which he also refused for this reason. He did not want to upset the Roman mob who really rule Rome. It is a show of modesty which is more like a show than reality.
good question he didnt want it