Does it make sense to find out that yields on some corporate bonds maturing after one or two years is lower than the yield on treasury bills?

no it does not make sense in the US or most European markets.you are probably looking at retail markets on the offer side. i am sure that the dealers are not bidding there. as an aside, at times, in some countries, libor rates have traded lower than gov't bond rates. in italy for example.

I would have to agree with apine that this does not make sense. This is especially true if we are talking about corporate bonds that are denominated in the same currency as the treasury bills (I wasn't sure if that was implied in your question or not). Theoretically, the treasury bill is a (default) risk-free security, especially if denominated in the local currency (i.e. the government can always print money to pay it off). In the strict sense, a corporate bond cannot have a rating that is lower than the government. When the government collapses, I doubt that there would be any investors that would be willing to buy stake in the local company. However, there are cases when there are companies that were able to get the same rating as the government (although this does not necessarily imply they can get the same yield, but very close), such as Petronas in Malaysia. But, as apine has said, in the US and most European markets, this is a highly unlikely event.