# Testing Cointegration at level or with first differences?

I have a question regarding testing for cointegration.

The situation is a follows: I have two time series that are both stationary at level when I consider "constant and trend". They are otherwise not stationary. The first differences are all stationary.

With regard to Cointegration testing: Do we test cointegration (Johansen) at level or at first differences? If we test with the level data, is it okay to model with a trend?

For example, in "urca" package in R, the function for the Johansen cointegration test is ca.jo. You may choose to specify the presence/absence of a deterministic time trend via the argument ecdet. There are more options controlled by other arguments, see here.