Context :

Aims : The Optical Gravitational Lensing Experiment ( OGLE ) , originally designed to search for microlensing events , provides a rich and uniform data set suitable for studying the variability of certain types of objects .
We used the OGLE data to study the photometry of central stars of planetary nebulae ( PNe ) in the Small Magellanic Cloud ( SMC ) .
In particular , we searched for close binary central stars with the aim to constrain the binary fraction and period distribution in the SMC .
We also searched for PNe mimics and removed them from the PNe sample .

Methods : We identified 52 counterparts of PNe in the SMC in the I-band images from the OGLE-II and OGLE-III surveys .
We analysed the time-series photometry of the PNe .
Spectra of the photometric variables were obtained to constrain the nature of the objects or search for additional evidence for binarity .

Results : Eight variables were found .
Of these , seven objects are PNe mimics , including one symbiotic star candidate .
One close binary central star of PN with a period of 1.15 or 2.31 day was discovered .
The obtained binary fraction for the SMC PNe and the observational biases are discussed in terms of the OGLE observations .

Conclusions :