We present spectra of a large sample of low-metallicity blue compact dwarf galaxies which exhibit broad components in their strong emission lines, mainly in Hbeta, [O III]4959, 5007 and Halpha. Twenty-three spectra have been obtained with the MMT, 14 of which show broad emission. The remaining 21 spectra with broad emission have been selected from the Data Release 5 of the Sloan Digital Sky Survey. The most plausible origin of broad line emission is the evolution of massive stars and their interaction with the circumstellar and interstellar medium. The broad emission with the lowest H$alpha$ luminosities (10^36 - 10^39 erg/s) is likely produced in circumstellar envelopes around hot Ofp/WN9 and/or LBV stars. The broad emission with the highest Halpha luminosities (10^40 - 10^42 erg/s) probably arises from type IIp or type IIn supernovae (SNe). It can also come from active galactic nuclei (AGN) containing intermediate-mass black holes, although we find no strong evidence for hard non-thermal radiation in our sample galaxies. The oxygen abundance in the host galaxies with SN candidates is low and varies in the range 12 + log O/H = 7.36 - 8.31. However, type IIn SN / AGN candidates are found only in galaxies with 12 + log O/H < 7.99. Spectroscopic monitoring of these type IIn SN / AGN candidates over a time scale of several years is necessary to distinguish between the two possibilities.
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