Muhić is accused of committing the criminal offense of fraud in office from January 6, 2019, to March 31, 2023, by providing false information about his presence at work and regular duties, as well as by submitting and approving false records of regular work. As an official in the institutions of Bosnia and Herzegovina, while performing the duties of the Consul General of Bosnia and Herzegovina in the Federal Republic of Germany, he aimed to obtain unlawful material gain.
The Prosecutor's Office of Bosnia and Herzegovina charged that, in this way, he misled the persons responsible for the finances of the Consulate General, who then made unlawful payments of salaries and other allowances and per diems to the accused. Through this method, he acquired unlawful material gain in an amount exceeding 50,000 BAM.
Began Muhić, as a member of the SDA, served as the Consul General of Bosnia and Herzegovina in Istanbul for the Republic of Turkey, Georgia, and Azerbaijan from 2015 to 2018.
In May 2023, he was elected mayor of Živinice in early elections that followed the death of Samir Kamenjaković.
Additionally, in October 2024, he declared victory in the race for the four-year term as mayor of Živinice.