They are hunting Lal Singh Arya, 53, who has been missing since Tuesday when a court ordered his arrest.
He is a suspect in the murder of an opposition politician in 2009 and has previously denied the charges.
Madhya Pradesh is the first and only state to have a department of happiness to boost the wellbeing of citizens.
The Bharatiya Janata Party-led government created the department in July 2016 and tasked it with ensuring "the happiness and tolerance of its citizens" by creating an "ecosystem that would enable people to realise their own potential of inner wellbeing".
Madhya Pradesh, India's second largest state, is home to more than 70 million people.
The department is supported by a State Institute of Happiness that is responsible for "developing tools of happiness", and thousand of "happiness volunteers" who conduct "happiness tutorials and programmes".
Mr Arya, who has headed the happiness department since its inception, heads five other departments, including aviation, general administration and welfare of scheduled castes and tribes.
He is scheduled to appear in court on 19 December.
"Police teams are looking for him. We are positive that we will track him down by then," local police told AFP.