A possible transit of HAT-P-13c has been predicted to occur on 2010 April 28. Here we report on the results of a multi-site campaign that has been organised to detect the event. CCD photometric observations have been carried out at five observatories in five countries. We reached 30% time coverage in a 5 days interval centered on the suspected transit of HAT-P-13c. Two transits of HAT-P-13b were also observed. No transit of HAT-P-13c has been detected while the campaign was on. By a numerical experiment with 10^5 model systems we conclude that HAT-P-13c is not a transiting exoplanet with a significance level from 65% to 72%, depending on the planet parameters and the prior assumptions. We present two times of transit of HAT-P-13b ocurring at BJD 2455141.5522 +- 0.0010 and BJD 2455249.4508 +- 0.0020. The TTV of HAT-P-13b is consistent with zero within 0.001 days. The refined orbital period of HAT-P-13b is 2.916293 +- 0.000010 days.
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