Aims: A possible transit of HAT-P-13c had been predicted to occur on 2010 April 28. Here we report on the results of our multi-site campaign organised to detect the event. Methods: CCD photometric observations were carried out at five observatories in five countries. We reached 30% time coverage in a 5-day interval centered on the suspected transit of HAT-P-13c. Two transits of HAT-P-13b were also observed. Results: No transit of HAT-P-13c was detected during the campaign. By a numerical experiment with 105 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 2 455 141.5522 ± 0.0010 and BJD 2 455 249.4508 ± 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. Photometric data are only available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/523/A84