You should check out Katy Pearce, an assistant professor of communication at University of Washington.  Her twitter handle (and she's very active there) is @katypearce.  She studies "tech & inequality in Armenia & Azerbaijan."  She's a social media guru and interested in Central Asia.  Although she may not look at Kazakhstan directly herself, she may know some research or generally be of some help.

Dear Mergen Dyussenov

The following are policy-related studies that may be of interest.

Kind regards,

Paul Chaney

Cooley, A. & Sharman, J.C.  (2015) Blurring the line between licit and illicit: transnational corruption networks in Central Asia and beyond, Central Asian Survey, Volume 34, Number 1, 2 January 2015, pp. 11-28.

Johnson, Erica (2014) Non-State Health Care Provision in Kazakhstan and Uzbekistan: Is Politicisation a Model? Europe-Asia Studies, Volume 66, Number 5, 28 May 2014, pp. 735-758(24)

Fighting Corruption in Transition Economies Kazakhstan: (Complete Edition ‐ ISBN 9264026142) OECD Governance, Volume 2007, Number 14, May 2007, pp. 1-179

Ingemar, Fägerlind; Kanaev Alexander, N.  2000 Redefining Citizenship Education in the Central Asian Countries, Educational Practice and Theory, Volume 22, Number 1, pp. 95-113

Duke, Trevor ; Keshishiyan, Elena ; Kuttumuratova, Aigul ; Ostergren, Mikael ; Ryumina, Irina ; Stasii, Ekaterina ; Weber, Martin W ; Tamburlini, Giorgio (2006) Quality of hospital care for children in Kazakhstan, Republic of Moldova, and Russia: systematic observational assessment, The Lancet,  Vol.367, pp.919-925

I would add:

Eric Gleave, Blaine Robbins, and Beth Kolko: Trust in Uzbekistan.

International Political Science Review, March 2012, 33: 209-229, first published on February 28, 2011. doi:10.1177/0192512110379491.

Article Trust in Uzbekistan

You may also find this of value

Cummings, S. N. and Nørgaard, O. (2004), Conceptualising State Capacity: Comparing Kazakhstan and Kyrgyzstan. Political Studies, 52: 685–708. doi: 10.1111/j.1467-9248.2004.00503.x