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I am using BLS labor productivity measures to estimate the impact of automation in the US. Looking through the BLS handbook and online, I haven't been able to determine if the LPC measures are in current dollars or constant dollars. Do you happen to know?

For example, the BLS reports Value of production by industry in $ millions. Is this a current-dollar or a constant-dollar measure?

BLS page on the topic & with access to data: http://www.bls.gov/lpc/

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It depends on which BLS numbers you look at

For example in Table 2 of http://www.bls.gov/opub/mlr/2013/article/industry-employment-and-output-projections-to-2022.htm it gives for manufacturing output:

Billions of chained 2005 dollars            Billions of dollars
      2002        2012                        2002        2012
    4,320.8     4,407.6                     3,848.3     5,604.8

and the first pair of numbers uses a constant dollar (more precisely a chain-weighted dollar) measure while the second pair uses a current dollar measure

For general productivity measures, the BLS says for example at http://www.bls.gov/opub/hom/pdf/homch12.pdf

Time-series indexes of manufacturing labor productivity (output per hour) and unit labor costs are constructed from three basic aggregate measures: Total real output, hours worked, and nominal compensation.

So output per hour aims at a real measure of productivity, while unit labor costs divide a nominal figure by a real figure to give something which combines real productivity and nominal wages

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